on relaxation algorithms in computation of noncooperative equilibria this paper considers a special class of numerical algorithms the so called relaxation algorithm for nash equilibrium points in noncooperative games the relaxation algorithms have been studied by various authors for the deterministic case convergence conditions of this algorithm are based on fixed point theorems for example basar 1987 and li and basar 1987 have proved its convergence for a two player game via the contraction mapping theorem for the quadratic case these conditions can be easily checked for other nonlinear payoff functions it is sometimes difficult to check these convergence conditions in this paper the authors propose an alternative approach using the residual terms of the nikaido isoda function the convergence theorem is proved for nonsmooth weakly convex concave nikaido isoda functions the family of weakly convex concave functions is broad enough for applications since if includes the family of smooth functions when the payoff functions are twice continuously differentiable the condition for the residual terms is reduced to strict positiveness of a matrix representing the difference of the hessians of the nikaido isoda function with respect to the first and second groups of variables an analogous condition was used by uryas ev 1988 to prove convergence of the gradient type algorithm for the nash equilibrium problem in this paper the authors discuss only the deterministic case nevertheless this approach can be generalized for the stochastic nash equilibrium problems with uncertainties in parameters

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

a semismooth equation approach to the solution of nonlinear complementarity problems in this paper we present a new algorithm for the solution of nonlinear complementarity problems the algorithm is based on a semismooth equation reformulation of the complementarity problem we exploit the recent extension of newton s method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions other interesting features of the new algorithm are an extreme simplicity along with a low computational burden per iteration we include numerical tests which show the viability of the approach

non linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass abstract a computational analysis of the non linear vibration and thermal post buckling of a heated orthotropic annular plate with a central rigid mass is examined for the cases of immovably hinged as well as clamped constraint conditions of the outer edge first based on von karman s plate theory and hamilton s principles the governing equations in terms of the displacements of the middle plane of the problem are derived then upon assuming that harmonic responses of the system exist the non linear partial differential equations are converted into the corresponding non linear ordinary differential equations through elimination of the time variable by using the kantorovich time averaging method finally by applying a shooting method the fundamental responses of the non linear vibration and thermal post buckling of the plate are numerically obtained for some prescribed values of the parameters such as the material rigidity ratio temperature rise and so on the curves of the fundamental frequency versus specified amplitude and the thermal post buckled equilibrium paths of the plate are numerically presented

generalized nash equilibrium problems and newton methods the generalized nash equilibrium problem where the feasible sets of the players may depend on the other players strategies is emerging as an important modeling tool however its use is limited by its great analytical complexity we consider several newton methods analyze their features and compare their range of applicability we illustrate in detail the results obtained by applying them to a model for internet switching

on structure and computation of generalized nash equilibria we consider generalized nash equilibrium problems gnep from a structural and computational point of view in gnep the players feasible sets may depend on the other players strategies moreover the players may share common constraints in particular the latter leads to the stable appearance of nash equilibria which are fritz john fj points but not karush kuhn tucker kkt points basic in our approach is the representation of fj points as zeros of an appropriate underdetermined system of nonsmooth equations here additional nonsmooth variables are taken into account we prove that the set of fj points together with corresponding active lagrange multipliers generically constitutes a lipschitz manifold its dimension is n 1 j 0 where n is the number of players and j 0 is the number of active common constraints in a structural analysis of nash equilibria the number n 1 j 0 plays a crucial role in fact the latter number encodes both the possible degeneracies for the players parametric subproblems and the dimension of the set of nash equilibria in particular in the nondegenerate case the dimension of the set of nash equilibria equals locally n 1 j 0 for the computation of fj points we propose a nonsmooth projection method npm which aims at nding solutions of an underdetermined system of nonsmooth equations npm is shown to be well dened for gnep local convergence of npm is conjectured for gnep under generic assumptions and its proof is challenging however we indicate special cases known from the literature in which convergence holds

a potential reduction newton method for constrained equations extending our previous work t wang r d c monteiro and j s pang math programming 74 1996 pp 159 195 this paper presents a general potential reduction newton method for solving a constrained system of nonlinear equations a major convergence result for the method is established specializations of the method to a convex semidefinite program and a monotone complementarity problem in symmetric matrices are discussed strengthened convergence results are established in the context of these specializations

an approximation scheme for a class of risk averse stochastic equilibrium problems we consider two models for stochastic equilibrium one based on the variational equilibrium of a generalized nash game and the other on the mixed complementarity formulation each agent in the market solves a single stage risk averse optimization problem with both here and now investment variables and production wait and see variables a shared constraint couples almost surely the wait and see decisions of all the agents an important characteristic of our approach is that the agents hedge risk in the objective functions on costs or profits of their optimization problems which has a clear economic interpretation this feature is obviously desirable but in the risk averse case it leads to variational inequalities with set valued operators a class of problems for which no established software is currently available to overcome this difficulty we define a sequence of approximating differentiable variational inequalities based on smoothing the nonsmooth risk measure in the agents problems such as average or conditional value at risk the smoothed variational inequalities can be tackled by the path solver for example the approximation scheme is shown to converge including the case when smoothed problems are solved approximately an interesting by product of our proposal is that the smoothing approach allows us to show existence of an equilibrium for the original problem to assess the proposed technique numerical results are presented the first set of experiments is on randomly generated equilibrium problems for which we compare the proposed methodology with the standard smooth reformulation of average value at risk minimization using additional variables to rewrite the associated max function the second set of experiments deals with a part of the real life european gas network for which dantzig wolfe decomposition can be combined with the smoothing approach

on the solution of the kkt conditions of generalized nash equilibrium problems we consider the solution of generalized nash equilibrium problems by concatenating the kkt optimality conditions of each player s optimization problem into a single kkt like system we then propose two approaches for solving this kkt system the first approach is rather simple and uses a merit function equation based technique for the solution of the kkt system the second approach partially motivated by the shortcomings of the first one is an interior point based method we show that this second approach has strong theoretical properties and in particular that it is possible to establish global convergence under sensible conditions this probably being the first result of its kind in the literature we discuss the results of an extensive numerical testing on four kkt based solution algorithms showing that the new interior point method is efficient and very robust

a pivotal method for affine variational inequalities we explain and justify a path following algorithm for solving the equations acx a where a is a linear transformation from rn to rn c is a polyhedral convex subset of rn and ac is the associated normal map when ac is coherently oriented we are able to prove that the path following method terminates at the unique solution of acx a which is a generalization of the well known fact that lemke s method terminates at the unique solution of lcpq m when m is a p matrix otherwise we identity two classes of matrices which are analogues of the class of copositive plus and l matrices in the study of the linear complementarity problem we then prove that our algorithm processes acx a when a is the linear transformation associated with such matrices that is when applied to such a problem the algorithm will find a solution unless the problem is infeasible in a well specified sense

aggregation and disaggregation in integer programming problems column aggregation of 0 1 programming problems is considered by relaxing the integer requirements in the aggregated problem an easy problem results the solution of which can be used to compute bounds on the loss of accuracy in the objective function value it is shown how these bounds can be improved by identification of valid inequalities and by exploiting primal degeneracy a small example is given to illustrate the procedure

finite element analysis of non linear vibration of a circular plate with a concentric rigid mass abstract a finite element analysis of non linear vibration of an elastic circular plate with a concentric rigid mass is examined for different cases of boundary conditions the non linear partial differential equations and the associated boundary conditions are derived from an energy method by using the hamiltonian principle the applications of the finite element method to the dynamic problem rely on the use of a variational principle to derive the necessary element properties or equations the assembled equations for the plate are formed by summing each element equation obtained in consideration of a single element then the boundary conditions are imposed on the vector of nodal field variables so that the appropriate boundary conditions are satisfied the assembled equations form an eigenvalue problem and are solved for the eigenvalues as well as the unknown field variables the relations between the fundamental frequencies and the amplitudes of non linear vibrations of the circular isotropic elastic plate with a concentric rigid mass are obtained the results agree well with the solutions obtained by the kantorovich averaging method also the results yield the upper bounds of the solution to the stated problem

continuous time penalty methods for nash equilibrium seeking of a nonsmooth generalized noncooperative game in this paper we propose centralized and distributed continuous time penalty methods to find a nash equilibrium for a generalized noncooperative game with shared inequality and equality constraints and private inequality constraints that depend on the player itself by using the l 1 penalty function we prove that the equilibrium of a differential inclusion is a normalized nash equilibrium of the original generalized noncooperative game and the centralized differential inclusion exponentially converges to the unique normalized nash equilibrium of a strongly monotone game suppose that the players can communicate with their neighboring players only and the communication topology can be represented by a connected undirected graph based on a leader following consensus scheme and singular perturbation techniques we propose distributed algorithms by using the exact l 1 penalty function and the continuously differentiable squared l 2 penalty function respectively the squared l 2 penalty function method works for games with smooth constraints and the exact l 2 penalty function works for certain scenarios the proposed two distributed algorithms converge to an neighborhood of the unique normalized nash equilibrium and an neighborhood of an approximated nash equilibrium respectively with being a positive constant for each 0 and each initial condition there exists an varepsilon such that for each 0 varepsilon varepsilon the convergence can be guaranteed where varepsilon is a parameter in the algorithm

piecewise affine parameterized value function based bilevel non cooperative games generalizing certain network interdiction games communicated to us by andrew liu and his collaborators this paper studies a bilevel non cooperative game wherein the objective function of each player s optimization problem contains a value function of a second level linear program parameterized by the first level variables in a non convex manner in the applied network interdiction games this parameterization is through a piecewise linear function that upper bounds the second level decision variable in order to give a unified treatment to the overall two level game where the second level problems may be minimization or maximization we formulate it as a one level game of a particular kind namely each player s objective function is the sum of a first level objective function a value function of a second level maximization problem whose objective function involves a difference of convex dc specifically piecewise affine parameterization by the first level variables this non convex parameterization is a major difference from the family of games with min max objectives discussed in facchinei et al comput optim appl 59 1 85 112 2014 wherein the convexity of the overall games is preserved in contrast the piecewise affine dc parameterization of the second level objective functions to be maximized renders the players combined first level objective functions non convex and non differentiable we investigate the existence of a first order stationary solution of such a game which we call a quasi nash equilibrium and study the computation of such a solution in the linear quadratic case by lemke s method using a linear complementarity formulation

computing b stationary points of nonsmooth dc programs motivated by a class of applied problems arising from physical layer based security in a digital communication system in particular by a secrecy sum rate maximization problem this paper studies a nonsmooth difference of convex dc minimization problem the contributions of this paper are i clarify several kinds of stationary solutions and their relations ii develop and establish the convergence of a novel algorithm for computing a d stationary solution of a problem with a convex feasible set that is arguably the sharpest kind among the various stationary solutions iii extend the algorithm in several directions including a randomized choice of the subproblems that could help the practical convergence of the algorithm a distributed penalty approach for problems whose objective functions are sums of dc functions and problems with a specially structured nonconvex dc constraint for the latter class of problems a pointwise slater constraint qualification is introduced that facilitates the ver

solving quasi variational inequalities via their kkt conditions we propose to solve a general quasi variational inequality by using its karush kuhn tucker conditions to this end we use a globally convergent algorithm based on a potential reduction approach we establish global convergence results for many interesting instances of quasi variational inequalities vastly broadening the class of problems that can be solved with theoretical guarantees our numerical testings are very promising and show the practical viability of the approach

feedback nash equilibria in linear quadratic difference games with constraints in this paper we consider a class of noncooperative n player finite horizon linear quadratic dynamic games with linear constraints we introduce a constrained feedback information structure and provide necessary and sufficient conditions for the existence of a constrained feedback nash equilibrium for this class of games we show that the constrained feedback nash equilibrium can be obtained from a feedback nash equilibrium associated with an unconstrained multi parametric linear quadratic game where the parameters satisfy an equilibrium property we show that this relation leads to a fixed point interpretation further under a few additional assumptions we show that these fixed points can be obtained as solutions of a single large scale linear complementarity problem thereby providing a method to compute the constrained feedback nash equilibria we illustrate our results with a numerical example

on the variational equilibrium as a refinement of the generalized nash equilibrium we are concerned with a class of games in which the players strategy sets are coupled by a shared constraint a widely employed solution concept for such generalized nash games is the generalized nash equilibrium gne the variational equilibrium ve facchinei kanzow 2007 is a specific kind of gne characterized by the solution of the variational inequality formed from the common constraint and the mapping of the gradients of player objectives our contribution is a theory that provides sufficient conditions for ensuring that the existence of a gne implies the existence of a ve in such an instance the ve is said to be a refinement of the gne for certain games these conditions are shown to be necessary this theory rests on a result showing the equality of the brouwer degree of two suitably defined functions whose zeros are the gne and ve respectively this theory has a natural extension to the primal dual space of strategies and lagrange multipliers corresponding to the shared constraint our results unify some known results pertaining to such equilibria and provide mathematical substantiation for ideas that were known to be appealing to economic intuition

asymmetric variational inequality problems over product sets applications and iterative methods in this paper we i describe how several equilibrium problems can be uniformly modelled by a finite dimensional asymmetric variational inequality defined over a cartesian product of sets and ii investigate the local and global convergence of various iterative methods for solving such a variational inequality problem because of the special cartesian product structure these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions the resulting decomposition schemes often have a natural interpretation as some adjustment processes

a class of dantzig wolfe type decomposition methods for variational inequality problems we consider a class of decomposition methods for variational inequalities which is related to the classical dantzig wolfe decomposition of linear programs our approach is rather general in that it can be used with certain types of set valued or nonmonotone operators as well as with various kinds of approximations in the subproblems of the functions and derivatives in the single valued case also subproblems may be solved approximately convergence is established under reasonable assumptions we also report numerical experiments for computing variational equilibria of the game theoretic models of electricity markets our numerical results illustrate that the decomposition approach allows to solve large scale problem instances otherwise intractable if the widely used path solver is applied directly without decomposition

constrained traffic equilibrium in routing we study noncooperative routing in which each user is faced with a multicriterion optimization problem formulated as the minimization of one criterion subject to constraints on others we address the questions of existence and uniqueness of equilibrium we show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem we obtain uniqueness in some weaker sense under appropriate conditions we show that the link utilizations are uniquely determined at equilibrium we further study the normalized constrained equilibrium and apply it to pricing

generalized nash games and quasi variational inequalities abstract a generalized nash game is an n person noncooperative game with nondisjoint strategy sets other names for this game form include social equilibria and pseudo nash games this paper explores both the qualitative and quantitative properties of such games through the use of quasi variational inequality theory several interesting relationships between the variational and quasi variational inequality forms of this class of games are described and the practical implementation of generalized nash games are explored at length

robust orthogonal complement principal component analysis abstractrecently the robustification of principal component analysis pca has attracted lots of attention from statisticians engineers and computer scientists in this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation based on a mathematical formulation of such transformed outliers a novel robust orthogonal complement principal component analysis roc pca is proposed the framework combines the popular sparsity enforcing and low rank regularization techniques to deal with row wise outliers as well as element wise outliers a nonasymptotic oracle inequality guarantees the accuracy and high breakdown performance of roc pca in finite samples to tackle the computational challenges an efficient algorithm is developed on the basis of stiefel manifold optimization and iterative thresholding furthermore a batch variant is proposed to significantly reduce the cost in ultra high dimensions th

a generalized iterative water filling algorithm for distributed power control in the presence of a jammer consider a scenario in which k users and a jammer share a common spectrum of n orthogonal tones both the users and the jammer have limited power budgets the goal of each user is to allocate its power across the n tones in such a way that maximizes the total sum rate that he she can achieve while treating the interference of other users and the jammer s signal as additive gaussian noise the jammer on the other hand wishes to allocate its power in such a way that minimizes the utility of the whole system that being the total sum of the rates communicated over the network for this noncooperative game we propose a generalized version of the existing iterative water filling algorithm whereby the users and the jammer update their power allocations in a greedy manner we study the existence of a nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water filling algorithm converges to a nash equilibrium of the game the conditions that we derive in this paper depend only on the system parameters and hence can be checked a priori simulations show that when the convergence conditions are violated the presence of a jammer can cause the otherwise convergent iterative water filling algorithm to oscillate

non linear vibration of a hinged circular plate with a concentric rigid mass abstract a computational analysis of the non linear vibration of a hinged elastic circular plate with a concentric rigid mass is examined for movable and immovable hinged cases the non linear partial differential equations are converted into the corresponding non linear ordinary differential equations by elimination of the time variable with a kantorovich time averaging method then by using a newton iteration technique and the concept of analytic continuation the solutions of the fundamental responses of the non linear vibration of the circular plate with a concentric rigid mass are obtained

a continuous time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows this paper formally introduces a linear complementarity system lcs formulation for a continuous time multi user class dynamic user equilibrium due model for the determination of trip timing decisions in a simplified single bottleneck model existence of a lipschitz solution trajectory to the model is established by a constructive time stepping method whose convergence is rigorously analyzed the solvability of the time discretized subproblems by lemke s algorithm is also proved combining linear complementarity with ordinary differential equations and being a new entry to the mathematical programming field the lcs provides a computational tractable framework for the rigorous treatment of the due problem in continuous time this paper makes a positive contribution in this promising research venue pertaining to the application of differential variational theory to dynamic traffic problems

joint sensing and power allocation in nonconvex cognitive radio games quasi nash equilibria in this paper we propose a novel class of nash problems for cognitive radio cr networks composed of multiple primary users pus and secondary users sus wherein each su player competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration the detection thresholds and the vector power allocation over a multichannel link in addition to power budget constraints several deterministic or probabilistic interference constraints can be accommodated in the proposed general formulation such as constraints on the maximum individual aggregate probabilistic interference tolerable from the pus to keep the optimization as decentralized as possible global interference constraints when present are imposed via pricing the prices are thus additional variables to be optimized the resulting players optimization problems are nonconvex and there are price clearance conditions associated with the nonconvex global interference constraints to be satisfied by the equilibria of the game which make the analysis of the proposed game a challenging task none of classical results in the game theory literature can be successfully applied to deal with the nonconvexity of the game we introduce a relaxed equilibrium concept the quasi nash equilibrium qne and study its main properties performance and connection with local nash equilibria quite interestingly the proposed game theoretical formulations yield a considerable performance improvement with respect to current centralized and decentralized designs of cr systems which validates the concept of qne

distributed power allocation with rate constraints in gaussian parallel interference channels this paper considers the minimization of transmit power in gaussian parallel interference channels subject to a rate constraint for each user to derive decentralized solutions that do not require any cooperation among the users we formulate this power control problem as a generalized nash equilibrium ne game we obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem then to compute the solutions of the game we propose two distributed algorithms based on the single user water filling solution the sequential and the simultaneous iterative water filling algorithms wherein the users update their own strategies sequentially and simultaneously respectively we derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms our results are applicable to all practical distributed multipoint to multipoint interference systems either wired or wireless where a quality of service in qos terms of information rate must be guaranteed for each link

newton s method for computing a normalized equilibrium in the generalized nash game through fixed point formulation we consider the generalized nash equilibrium problem gnep where not only the players cost functions but also their strategy spaces depend on the rivals decision variables existence results for gneps are typically shown by using a fixed point argument for a certain set valued function here we use a regularization of this set valued function in order to obtain a single valued function that is easier to deal with from a numerical point of view we show that the fixed points of the latter function constitute an important subclass of the generalized equilibria called normalized equilibria this fixed point formulation is then used to develop a nonsmooth newton method for computing a normalized equilibrium the method uses a so called computable generalized jacobian that is much easier to compute than clarke generalized jacobian or b subdifferential we establish local superlinear quadratic convergence of the method under the constant rank constraint qualification which is weaker than the frequently used linear independence constraint qualification and a suitable second order condition some numerical results are presented to illustrate the performance of the method

a noncooperative game approach to osnr optimization in optical networks we consider a game theory framework for power control in optical networks channel optical signal to noise ratio osnr optimization is formulated as an m player noncooperative game based on a general network osnr model conditions for existence and uniqueness of the game equilibrium solution are given an iterative algorithm for power control is proposed that uses only channel specific feedback measurements and is shown to converge to the equilibrium solution

two stage non cooperative games with risk averse players this paper formally introduces and studies a non cooperative multi agent game under uncertainty the well known nash equilibrium is employed as the solution concept of the game while there are several formulations of a stochastic nash equilibrium problem we focus mainly on a two stage setting of the game wherein each agent is risk averse and solves a rival parameterized stochastic program with quadratic recourse in such a game each agent takes deterministic actions in the first stage and recourse decisions in the second stage after the uncertainty is realized each agent s overall objective consists of a deterministic first stage component plus a second stage mean risk component defined by a coherent risk measure describing the agent s risk aversion we direct our analysis towards a broad class of quantile based risk measures and linear quadratic recourse functions for this class of non cooperative games under uncertainty the agents objective functions can be shown to be convex in their own decision variables provided that the deterministic component of these functions have the same convexity property nevertheless due to the non differentiability of the recourse functions the agents objective functions are at best directionally differentiable such non differentiability creates multiple challenges for the analysis and solution of the game two principal ones being 1 a stochastic multi valued variational inequality is needed to characterize a nash equilibrium provided that the players optimization problems are convex 2 one needs to be careful in the design of algorithms that require differentiability of the objectives moreover the resulting multi valued variational formulation cannot be expected to be of the monotone type in general the main contributions of this paper are as follows a prior to addressing the main problem of the paper we summarize several approaches that have existed in the literature to deal with uncertainty in a non cooperative game b we introduce a unified formulation of the two stage snep with risk averse players and convex quadratic recourse functions and highlight the technical challenges in dealing with this game c to handle the lack of smoothness we propose smoothing schemes and regularization that lead to differentiable approximations d to deal with non monotonicity we impose a generalized diagonal dominance condition on the players smoothed objective functions that facilitates the application and ensures the convergence of an iterative best response scheme e to handle the expectation operator we rely on known methods in stochastic programming that include sampling and approximation f we provide convergence results for various versions of the best response scheme particularly for the case of private recourse functions overall this paper lays the foundation for future research into the class of sneps that provides a constructive paradigm for modeling and solving competitive decision making problems with risk averse players facing uncertainty this paradigm is very much at an infancy stage of research and requires extensive treatment in order to meet its broad applications in many engineering and economics domains

on the solution of affine generalized nash equilibrium problems with shared constraints by lemke s method affine generalized nash equilibrium problems agneps represent a class of non cooperative games in which players solve convex quadratic programs with a set of linear constraints that couple the players variables the generalized nash equilibria gne associated with such games are given by solutions to a linear complementarity problem lcp this paper treats a large subclass of agneps wherein the coupled constraints are shared by i e common to the players specifically we present several avenues for computing structurally different gne based on varying consistency requirements on the lagrange multipliers associated with the shared constraints traditionally variational equilibria ve have been amongst the more well studied gne and are characterized by a requirement that the shared constraint multipliers be identical across players we present and analyze a modification to lemke s method that allows us to compute gne that are not necessarily ve if successful the modified method computes a partial variational equilibrium characterized by the property that some shared constraints are imposed to have common multipliers across the players while other are not so imposed trajectories arising from regularizing the lcp formulations of agneps are shown to converge to a particular type of gne more general than rosen s normalized equilibrium that in turn includes a variational equilibrium as a special case a third avenue for constructing alternate gne arises from employing a novel constraint reformulation and parameterization technique the associated parametric solution method is capable of identifying continuous manifolds of equilibria numerical results suggest that the modified lemke s method is more robust than the standard version of the method and entails only a modest increase in computational effort on the problems tested finally we show that the conditions for applying the modified lemke s scheme are readily satisfied in a breadth of application problems drawn from communication networks environmental pollution games and power markets

geometrically nonlinear vibrations of rectangular plates carrying a concentrated mass abstract nonlinear forced vibrations of rectangular plates carrying a central concentrated mass are studied the plate is assumed to have immovable edges and rotational springs numerical results are presented for clamped plates the von karman nonlinear plate theory is used but in plane inertia in both the plate and the mass is retrained the problem is discretized into a multi degree of freedom dof system by using an energy approach and lagrange equations taking damping into account a pseudo arclength continuation method is used in order to obtain numerical solutions results are presented as both i frequency amplitude curves and ii time domain responses the effect of gravity and the effect of the consequent initial plate deflection are also investigated

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

approximations of nash equilibria inspired by previous works on approximations of optimization problems and recent papers on the approximation of walrasian and nash equilibria and on stochastic variational inequalities the present paper investigates the approximation of nash equilibria and clarifies the conditions required for the convergence of the approximate equilibria via a direct approach a variational approach and an optimization approach besides directly addressing the issue of convergence of nash equilibria via approximation our investigation leads to a deeper understanding of various notions of functional convergence and their interconnections more importantly the investigation yields improved conditions for convergence of the approximate nash equilibria via the variational approach an illustrative application of our results to the approximation of a nash equilibrium in a competitive capacity expansion model under uncertainty is presented

lopsided convergence an extension and its quantification much of the development of lopsided convergence for bifunctions defined on product spaces was in response to motivating applications a wider class of applications requires an extension that would allow for arbitrary domains not only product spaces this leads to an extension of the definition and its implications that include the convergence of solutions and optimal values of a broad class of minsup problems in the process we relax the definition of lopsided convergence even for the classical situation of product spaces we now capture applications in optimization under stochastic ambiguity generalized nash games and many others we also introduce the lop distance between bifunctions which leads to the first quantification of lopsided convergence this quantification facilitates the study of convergence rates of methods for solving a series of problems including minsup problems generalized nash games and various equilibrium problems

an extension of duality to a game theoretic framework this paper extends some duality results from a standard optimization setup to a noncooperative nash game framework a nash game ng with coupled constraints is considered solving directly such a coupled ng requires coordination among possibly all players an alternative approach is proposed based on its relation to a special constrained optimization problem for the ng game cost function with respect to the second argument that admits a fixed point solution specific separability properties of the ng game cost are exploited and duality results are developed this duality extension leads naturally to a hierarchical decomposition into a lower level ng with no coupled constraints and a higher level system optimization problem in the second part of the paper these theoretical results are applied to a coupled ng with coupled constraints as encountered in optical networks

a robust trust region method for constrained nonlinear programming problems most of the published work on trust region algorithms for constrained optimization is derived from the original work of fletcher on trust region algorithms for nondifferentiable exact penalty functions these methods are restricted to applications where a reasonable estimate of the magnitude of an optimal kuhn tucker multiplier vector can be given more recently an effort has been made to extend the trust region methodology to the sequential quadratic programming sqp algorithm of wilson han and powell all of these extensions to the wilson han powell sqp algorithm consider only the equality constrained case and require strong global regularity hypotheses this paper presents a general framework for trust region algorithms for constrained problems that does not require such regularity hypotheses and allows very general constraints the approach is modeled on the one given by powell for convex composite optimization problems and is driven by linear subproblems that yield viable estimates for the value o

distributed algorithms for aggregative games on graphs we consider a class of nash games termed as aggregative games being played over a networked system in an aggregative game a player s objective is a function of the aggregate of all the players decisions every player maintains an estimate of this aggregate and the players exchange this information with their local neighbors over a connected network we study distributed synchronous and asynchronous algorithms for information exchange and equilibrium computation over such a network under standard conditions we establish the almost sure convergence of the obtained sequences to the equilibrium point we also consider extensions of our schemes to aggregative games where the players objectives are coupled through a more general form of aggregate function finally we present numerical results that demonstrate the performance of the proposed schemes

distributed power control for one to many transmissions in gaussian interference channels in this paper we extend the distributed power control problem for one to one transmissions in gaussian interference channels to one to many transmission scenarios we assume a user centric wireless network where the end users play the roles of decision makers we formulate the power control problem as a noncooperative game new challenges arise due to the coupling issues among power strategy spaces of distributed end users which make standard nash equilibrium based noncooperative game approach inapplicable indeed our problem turns out to be a generalized nash equilibrium problem gnep resorting to variational inequality theory we show several fundamental properties of the gnep then we propose a penalty based distributed algorithm ip 2ja which possesses favorable properties for practical implementation numerical results are provided to verify our arguments and proposed algorithm

differential variational inequality approach to dynamic games with shared constraints the dynamic nash equilibrium problem with shared constraints nepsc involves a dynamic decision process with multiple players where not only the players cost functionals but also their admissible control sets depend on the rivals decision variables through shared constraints for a class of the dynamic nepsc we propose a differential variational inequality formulation using this formulation we show the existence of solutions of the dynamic nepsc and develop a regularized smoothing method to find a solution of it we prove that the regularized smoothing method converges to the least norm solution of the differential variational inequality which is a solution of the dynamic nepsc as the regularization parameter lambda and smoothing parameter mu go to zero with the order mu o lambda o numerical examples are given to illustrate the existence and convergence results

applications of degree theory to linear complementarity problems in this paper we consider two applications of degree theory to linear complementarity problems in the first application we study the stability of an lcp at a solution point specifically we prove the stability of an lcp corresponding to a p0 matrix at an isolated solution using a recent degree formula due to stewart 1991 we strengthen a stability result of gowda and pang 1992 in the second application we use the same degree formula of stewart to describe the number of solutions of lcpm q when m is a negative almost n matrix this analysis leads to a lipschitzian characterization of the solution map i q solm q corresponding to a nondegenerate negative matrix

open loop and feedback nash equilibria in constrained linear quadratic dynamic games played over event trees abstract we characterize open loop and feedback nash equilibria for a class of constrained linear quadratic multistage games having the following features a the control variables are of two types namely control variables that enter the dynamics but are not constrained and control variables that are part of state control constraints but do not enter the dynamics b the parameter values are uncertain with the stochastic process being described by a event tree this paper takes stock on reddy and zaccour 2015 2017 where the same class of games was considered but in a deterministic setting here we follow the same approaches and rewrite the results in these two papers in a stochastic setting

technical note an improved dual based algorithm for the generalized assignment problem the generalized assignment problem gap determines the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent subject to an agent s capacity existing solution algorithms have not solved problems with more than 100 decision variables this paper designs an optimization algorithm for the gap that effectively solves problems with up to 500 variables compared with existing procedures this algorithm requires fewer enumeration nodes and shorter running times improved performance stems from an enhanced lagrangian dual ascent procedure that solves a lagrangian dual at each enumeration node adding a surrogate constraint to the lagrangian relaxed model and an elaborate branch and bound scheme an empirical investigation of various problem structures not considered in existing literature is also presented

local indices for degenerate variational inequalities we provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function f over a convex set m represented by a finite number of inequality constraints our index formula can be applied when the solutions are nonsingular and possibly degenerate as long as they also satisfy the injective normal map inm property which is implied by strong stability we show that when the inm property holds the degeneracy in a solution can be removed by perturbing the function f slightly i e the index of a degenerate solution is equal to the index of a nondegenerate solution of a slightly perturbed variational inequality problem we further show that our definition of the index is equivalent to the topological index of the normal map at the zero corresponding to the solution as an application of our index formula we provide a global index theorem for variational inequalities which holds even when the solutions are degenerate

distributed nash equilibrium seeking this paper presents an asynchronous gossip based algorithm for finding a nash equilibrium ne of a game in a distributed multi player network the algorithm is designed in such a way that players make decisions based on estimates of the other players actions obtained from local neighbors using a set of standard assumptions on the cost functions and communication graph the paper proves almost sure convergence to a ne for diminishing step sizes for constant step sizes an error bound on expected distance from a ne is established the effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes

a multiplier adjustment method for the generalized assignment problem we describe a branch and bound algorithm for the generalized assignment problem in which bounds are obtained from a lagrangian relaxation with the multipliers set by a heuristic adjustment method the algorithm was tested on a large sample of small random problems and a number of large problems derived from a vehicle routing application computation times were reasonable in all cases and the branch and bound trees generated had nearly two orders of magnitude fewer nodes than for competing algorithms although comparison of running times on different machines is difficult the multiplier adjustment method appears to be about one order of magnitude faster than the best previously existing algorithms for this problem

distributed learning for stochastic generalized nash equilibrium problems this paper examines a stochastic formulation of the generalized nash equilibrium problem where agents are subject to randomness in the environment of unknown statistical distribution we focus on fully distributed online learning by agents and employ penalized individual cost functions to deal with coupled constraints three stochastic gradient strategies are developed with constant step sizes we allow the agents to use heterogeneous step sizes and show that the penalty solution is able to approach the nash equilibrium in a stable manner within o mu text max for small step size value mu text max and sufficiently large penalty parameters the operation of the algorithm is illustrated by considering the network cournot competition problem

divide to conquer decomposition methods for energy optimization modern electricity systems provide a plethora of challenging issues in optimization the increasing penetration of low carbon renewable sources of energy introduces uncertainty in problems traditionally modeled in a deterministic setting the liberalization of the electricity sector brought the need of designing sound markets ensuring capacity investments while properly reflecting strategic interactions in all these problems hedging risk possibly in a dynamic manner is also a concern the fact of representing uncertainty and or competition of different companies in a multi settlement power market considerably increases the number of variables and constraints for this reason usually a trade off needs to be found between modeling and numerical tractability the more details are brought into the model the harder becomes the optimization problem for structured optimization and generalized equilibrium problems we explore some variants of solution methods based on lagrangian relaxation and on benders decomposition throughout we keep as a leading thread the actual practical value of such techniques in terms of their efficiency to solve energy related problems

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

design of cognitive radio systems under temperature interference constraints a variational inequality approach the concept of cognitive radio cr has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed primary and unlicensed secondary users in the same bandwidth in this paper we propose a novel nash equilibrium ne problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate the formulation contains constraints on the transmit power and possibly spectral masks as well as aggregate interference tolerable at the primary users receivers the coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of nash games that cannot be addressed using the game theoretical models proposed in the literature for this purpose we need the framework given by the more advanced theory of finite dimensional variational inequalities vi this provides us with all the mathematical tools necessary to analyze the proposed ne problem e g existence and uniqueness of the solution and to devise alternative distributed algorithms along with their convergence properties

spatial oligopolistic equilibria with arbitrage shared resources and price function conjectures this paper considers equilibria among multiple firms that are competing non cooperatively against each other to sell electric power and buy resources needed to produce that power examples of such resources include fuels power plant sites and emissions allowances the electric power market is a spatial market on a network in which flows are constrained by kirchhoff s current and voltage laws arbitragers in the power market erase spatial price differences that are non cost based power producers can compete in power markets a la cournot game in quantities or in a generalization of the cournot game termed the conjectured supply function game in which they anticipate that rivals will respond to price changes in input markets producers either compete a la bertrand price taking behavior or they can conjecture that price will increase with consumption of the resource the simultaneous competition in power and input markets presents opportunities for strategic price behavior that cannot be analyzed using models of power markets alone depending on whether the producers treat the arbitrager endogenously or exogenously we derive two mixed nonlinear complementarity formulations of the oligopolistic problem we establish the existence and uniqueness of solutions as well as connections among the solutions to the model formulations a numerical example is provided for illustrative purposes

nash cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints most previous nash cournot models of competition among electricity generators have assumed smooth demand price functions facilitating computation and proofs of existence and uniqueness however nonsmooth demand functions are an important feature of real power markets due for example to price caps and generator recognition of transmission constraints that limit exports a more general model of nash cournot competition on networks is proposed that accounts for these features by including 1 concave piecewise linear demand curves and 2 joint constraints that include variables from other generating companies within the profit maximization problems for individual generators the piecewise demand curves imply in general a nonmonotone multivalued variational inequality problem thus for instance imposition of a price cap can destroy the uniqueness properties found in previous models so that distinct solutions can yield different sets of profits for market participants the joint constraints turn the equilibrium problem into a quasi variational inequality which also can yield multiple solutions the formulation poses computational challenges that can cause lemke s algorithm to fail a restricted formulation is proposed that can be solved by that algorithm

nonconvex games with side constraints this paper develops an optimization based theory for the existence and uniqueness of equilibria of a noncooperative game wherein the selfish players optimization problems are nonconvex and there are side constraints and an associated price clearance to be satisfied by the equilibria a new concept of equilibrium for such a nonconvex game which we term a quasi nash equilibrium qne is introduced as a solution of the variational inequality vi obtained by aggregating the first order optimality conditions of the players problems while retaining the convex constraints if any in the defining set of the vi under a second order sufficiency condition from nonlinear programming a qne becomes a local nash equilibrium of the game uniqueness of a qne is established using a degree theoretic proof under a key boundedness property of the karush kuhn tucker multipliers of the nonconvex constraints and the positive definiteness of the hessians of the players lagrangian functions we establish the single valuedness of the players best response maps from which the existence of a nash equilibrium ne of the nonconvex game follows we also present a distributed algorithm for computing an ne of such a game and provide a matrix theoretic condition for the convergence of the algorithm an application is presented that pertains to a special multi leader follower game wherein the nonconvexity is due to the followers equilibrium conditions in the leaders optimization problems another application to a cognitive radio paradigm in a signal processing game is described in detail in g scutari and j s pang ieee trans inform theory submitted j s pang and g scutari joint ieee trans signal process submitted

games with coupled propagated constraints in optical networks with multi link topologies we consider games in optical networks in the class of m player games with coupled utilities and constraints nash equilibria of such games can be computed based on recent extension of duality to a game theoretical framework this work extends previous results on games with coupled constraints in optical links to multi link topologies coupled constraints in optical networks are propagated along links which introduces additional complexities for analysis specifically convexity of the propagated constraints is no longer automatically ensured we show that convexity is satisfied for single sink multi link topologies the general case of multi links with arbitrary sources and sinks is dealt with by a partitioned game with stages we exploit the single sink structure of each stage and the ladder nested form of the game and we discuss iterative computation of equilibria based on a three level hierarchical algorithm and prove its convergence under certain conditions

liquidity risks on power exchanges a generalized nash equilibrium model the extreme volatility of electricity prices makes their financial derivatives important instruments for asset managers even if the volume of derivative contracts traded on power exchanges has been growing since the inception of the restructuring of the sector electricity remains considerably less liquid than other commodity markets this paper assesses the effect of limited liquidity in power exchanges using an equilibrium model where agents cannot hedge up to their desired level mathematically the problem is formulated as a two stage stochastic generalized nash equilibrium with possibly multiple equilibria computing a large panel of solutions we show how the risk premium and players profits are affected by illiquidity we also dhow that the illiquidity in the ftr market affects the trades in the electricity futures market

vi constrained hemivariational inequalities distributed algorithms and power control in ad hoc networks we consider centralized and distributed algorithms for the numerical solution of a hemivariational inequality hvi where the feasible set is given by the intersection of a closed convex set with the solution set of a lower level monotone variational inequality vi the algorithms consist of a main loop wherein a sequence of one level strongly monotone hvis are solved that involve the penalization of the non vi constraint and a combination of proximal and tikhonov regularization to handle the lower level vi constraints minimization problems possibly with nonconvex objective functions over implicitly defined vi constraints are discussed in detail the methods developed in the paper are then used to successfully solve a new power control problem in ad hoc networks

maximal covering code multiplexing access telecommunication networks abstract we present a maximal covering model for the network design of code division multiplexing access cdma telecommunication system properties of the solution and the algorithm have been studied the model has been developed to solve actual problems they are extremely large so exact decomposition methods cannot be used to solve it a lagrangian decomposition heuristic has been defined different algorithm options have been computationally compared using random generated and actual data model and algorithm parameters have been adjusted and sensibility of the solution to the data has been considered in these tests

real and complex monotone communication games noncooperative game theoretic tools have been increasingly used to study many important resource allocation problems in communications networking smart grids and portfolio optimization in this paper we consider a general class of convex nash equilibrium problems neps where each player aims at solving an arbitrary smooth convex optimization problem differently from most of current works we do not assume any specific structure for the players problems and we allow the optimization variables of the players to be matrices in the complex domain our main contribution is the design of a novel class of distributed asynchronous best response algorithms suitable for solving the proposed neps even in the presence of multiple solutions the new methods whose convergence analysis is based on variational inequality vi techniques can select among all the equilibria of a game those that optimize a given performance criterion at the cost of limited signaling among the players this is a major departure from existing best response algorithms whose convergence conditions imply the uniqueness of the ne some of our results hinge on the use of vi problems directly in the complex domain the study of these new kind of vis also represents a noteworthy innovative contribution we then apply the developed methods to solve some new generalizations of single input single output siso and multiple input multiple output mimo games in cognitive radio systems showing a considerable performance improvement over classical pure noncooperative schemes

sample average approximation method for a class of stochastic generalized nash equilibrium problems we consider a class of stochastic generalized nash equilibrium problems sgneps under some mild conditions we reformulate the sgnep as a stochastic mixed complementarity problem smcp we apply the well known sample average approximation saa method to solve the smcp we further introduce an interior point method to solve the saa problems comprehensive convergence analysis is given as well in addition we demonstrate the proposed approach on a stochastic generalized nash equilibrium model in river basin pollution game

a nested noncooperative osnr game in distributed wdm optical links this paper develops a nash game formulation for optical signal to noise ratio osnr in distributed optical links the starting point is a recent network osnr model developed for optically amplified links whereby channel powers are adjusted independently only at transmitter sites a more general case is considered here where channel powers are also adjustable at intermediary dynamic sites specific to optical networks for this inherent distributed configuration a nested nash game is formulated towards minimizing channel osnr degradation along the link existence and uniqueness of the nash equilibrium solution is shown and a recursive procedure for constructing it is given based on this an iterative algorithm that is distributed with respect to both channels and spans is proposed

penalty methods for the solution of generalized nash equilibrium problems the generalized nash equilibrium problem gnep is an extension of the classical nash equilibrium problem where both the objective functions and the constraints of each player may depend on the rivals strategies this class of problems has a multitude of important engineering applications and yet solution algorithms are extremely scarce in this paper we analyze in detail a globally convergent penalty method that has favorable theoretical properties we also consider strengthened results for a particular subclass of problems very often considered in the literature basically our method reduces the gnep to a single penalized and nonsmooth nash equilibrium problem we suggest a suitable method for the solution of the latter penalized problem and present extensive numerical results

a new lagrangian relaxation approach to the generalized assignment problem abstract in this paper we present a new lagrangian relaxation approach to the generalized assignment problem gap the new approach is based on a reformulation of gap into an equivalent problem which is then relaxed by traditional lagrangian relaxation techniques the reformulation is created by introducing a set of auxiliary variables and a number of coupling constraints by relaxing the coupling constraints we get subproblems where both types of constraint structures present in the gap are active the lower bound from the lagrangian dual of this approach is shown to be at least as strong as that from the best of the traditional lagrangian relaxation approaches an important feature is also the possibility of generating upper bounds quite easily the new approach has been tested on 10 problems of size m 4 n 25 i e 100 0 1 variables and the results have been compared with the traditional approaches

some lcps solvable in strongly polynomial time with lemke s algorithm we identify a class of linear complementarity problems lcps that are solvable in strongly polynomial time by lemke s algorithm scheme 1 or by the parametric principal pivoting method pppm this algorithmic feature for the class of problems under consideration here is attributable to the proper selection of the covering vector in scheme 1 or the parametric direction vector in the pppm which leads to solutions of limited and monotonically increasing support size such solutions are sparse these and other lcps may very well have multiple solutions many of which are unattainable by either algorithm and thus are said to be elusive the initial conditions imposed on the new matrix class identified in sect 2 are subsequently relaxed in later sections

repeated games duality and the central limit theorem this paper is concerned with the repeated zero sum games with one sided information and standard signaling we introduce here dual games that allow us to analyze the markovian behavior of the uninformed player and to explicitly compute his optimal strategies we then apply our results on the dual games to explain the appearance of the normal density in the n 1 2 term of the asymptotic expansion of vn as a consequence of the central limit theorem

solving large scale generalized assignment problems an aggregation disaggregation approach abstract in this paper large scale generalized assignment problems are considered we propose an approximation technique where the original full size programming problem is aggregated into a problem of more moderate size feasible solutions are generated through a disaggregation approach coupled with some complementing heuristics an upper bound on the loss of accuracy is also calculated a small test problem is solved in order to illustrate the idea and computational results from two larger problems is presented

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

three modeling paradigms in mathematical programming celebrating the sixtieth anniversary since the zeroth international symposium on mathematical programming was held in 1949 this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field these are competition dynamics and hierarchy the discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive equilibrium and nonlinear programming and variational inequalities we will describe the modeling approaches mathematical formulations and recent results of these paradigms and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field

on the multiplier penalty approach for quasi variational inequalities the multiplier penalty approach is one of the classical methods for the solution of constrained optimization problems this method was generalized to the solution of quasi variational inequalities by pang and fukushima comput manag sci 2 21 56 2005 based on the recent improvements achieved for the multiplier penalty approach for optimization we generalize the method by pang and fukushima for quasi variational inequalities in several respects a we allow to compute inexact kkt points of the resulting subproblems b we improve the existing convergence theory c we investigate some special classes of quasi variational inequalities where the resulting subproblems turn out to be easy to solve some numerical results indicate that the corresponding method works quite reliable in practice

joint sensing and power allocation in nonconvex cognitive radio games nash equilibria and distributed algorithms in this paper we propose a novel class of nash problems for cognitive radio cr networks modeled as gaussian frequency selective interference channels wherein each secondary user su competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration the detection thresholds and the vector power allocation the proposed general formulation allows us to accommodate several transmit power and deterministic probabilistic interference constraints such as constraints on the maximum individual and or aggregate probabilistic interference tolerable at the primary receivers to keep the optimization as decentralized as possible global coupling interference constraints are imposed by penalizing each su with a set of time varying prices based upon his contribution to the total interference the prices are thus additional variable to optimize the resulting players optimization problems are nonconvex moreover there are possibly price clearing conditions associated with the global constraints to be satisfied by the solution all this makes the analysis of the proposed games a challenging task none of classical results in the game theory literature can be successfully applied the main contribution of this paper is to develop a novel optimization based theory for studying the proposed nonconvex games we provide a comprehensive analysis of the existence and uniqueness of a standard nash equilibrium devise alternative best response based algorithms and establish their convergence some of the proposed algorithms are totally distributed and asynchronous whereas some others require limited signaling among the sus in the form of consensus algorithms in favor of better performance overall they are thus applicable to a variety of cr scenarios either cooperative or noncooperative which allows the sus to explore the existing tradeoff between signaling and performance

a penalized fischer burmeister ncp function we introduce a new ncp function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations this new ncp function turns out to have stronger theoretical properties than the widely used fischer burmeister function and other ncp functions suggested previously moreover numerical experience indicates that a semismooth newton method based on this new ncp function performs considerably better than the corresponding method based on the fischer burmeister function

efficiency loss in a network resource allocation game we explore the properties of a congestion game in which users of a congested resource anticipate the effect of their actions on the price of the resource when users are sharing a single resource we establish that the aggregate utility received by the users is at least 3 4 of the maximum possible aggregate utility we also consider extensions to a network context where users submit individual payments for each link in the network they may wish to use in this network model we again show that the selfish behavior of the users leads to an aggregate utility that is no worse than 3 4 of the maximum possible aggregate utility we also show that the same analysis extends to a wide class of resource allocation systems where end users simultaneously require multiple scarce resources these results form part of a growing literature on the price of anarchy i e the extent to which selfish behavior affects system efficiency

a new decomposition method for multiuser dc programming and its applications we propose a novel decomposition framework for the distributed optimization of difference convex dc type nonseparable sum utility functions subject to coupling convex constraints a major contribution of the paper is to develop for the first time a class of inexact best response like algorithms with provable convergence where a suitably convexified version of the original dc program is iteratively solved the main feature of the proposed successive convex approximation method is its decomposability structure across the users which leads naturally to distributed algorithms in the primal and or dual domain the proposed framework is applicable to a variety of multiuser dc problems in different areas ranging from signal processing to communications and networking as a case study in the second part of the paper we focus on two examples namely i a novel resource allocation problem in the emerging area of cooperative physical layer security and ii and the renowned sum rate maximization of mimo cognitive radio networks our contribution in this context is to devise a class of easy to implement distributed algorithms with provable convergence to stationary solution of such problems numerical results show that the proposed distributed schemes reach performance close to and sometimes better than that of centralized methods