exact penalty results for mathematical programs with vanishing constraints a mathematical program with vanishing constraints mpvc is a constrained optimization problem arising in certain engineering applications the feasible set has a complicated structure so that the most familiar constraint qualifications are usually violated this in turn implies that standard penalty functions are typically non exact for mpvcs we therefore develop a new mpvc tailored penalty function which is shown to be exact under reasonable assumptions this new penalty function can then be used to derive or recover suitable optimality conditions for mpvcs

vector nonsmooth variational like inequalities and optimization problems abstract in this paper we first extend the concepts of clarke s generalized derivation and subdifferential for a function whose domain is a subset of a metrizable topological vector space we also introduce and consider a new class of variational like inequalities which are called the vector nonsmooth variational like inequalities we also establish the relationship between the nonsmooth variational like inequalities and vector optimization problems under some suitable conditions in particular our results extend and generalize the results of mishra and wang s k mishra s y wang vector variational like inequalities and nonsmooth vector optimization problems nonlinear anal 64 2006 1939 1945 and mishra and noor s k mishra m aslam noor on vector variational like inequality problems j math anal appl 311 2005 69 75

an iterative scheme for a class of quasi variational inequalities an iterative scheme is given to obtain the approximate solution of a class of quasi variational inequalities it is shown that the approximate solution obtained by the iterative scheme converges strongly in the hilbert space to the exact solution as a special case we obtain the corresponding iterative scheme for variational inequalities

logarithmic lower bounds in the cell probe model we develop a new technique for proving cell probe lower bounds on dynamic data structures this technique enables us to prove an amortized randomized omega lg n lower bound per operation for several data structural problems on n elements including partial sums dynamic connectivity among disjoint paths or a forest or a graph and several other dynamic graph problems by simple reductions such a lower bound breaks a long standing barrier of omega lg n lg lg n for any dynamic language membership problem it also establishes the optimality of several existing data structures such as sleator and tarjan s dynamic trees we also prove the first omega log b n lower bound in the external memory model without assumptions on the data structure such as the comparison model our lower bounds also give a query update trade off curve matched e g by several data structures for dynamic connectivity in graphs we also prove matching upper and lower bounds for partial sums when parameterized by the word size and the maximum additive change in an update

strong duality and kkt conditions in nonconvex optimization with a single equality constraint and geometric constraint some topological and geometric characterizations of strong duality for a non convex optimization problem under a single equality and geometric constraints are established in particular a hidden convexity of the conic hull of joint range of the pair of functions associated to the original problem is obtained applications to derive a characterization of the validity of kkt conditions without standard constraints qualification are also discussed it goes beyond the exact penalization technique several examples showing our results provide much more information than those appearing elsewhere are given finally the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail

shape optimization in contact problems with coulomb friction the paper deals with a discretized problem of the shape optimization of elastic bodies in unilateral contact the aim is to extend existing results to the case of contact problems following the coulomb friction law mathematical modelling of the coulomb friction problem leads to a quasi variational inequality it is shown that for small coefficients of friction the discretized problem with coulomb friction has a unique solution and that this solution is lipschitzian as a function of a control variable describing the shape of the elastic body the shape optimization problem belongs to a class of so called mathematical programs with equilibrium constraints mpecs the uniqueness of the equilibria for fixed controls enables us to apply the so called implicit programming approach its main idea consists of minimizing a nonsmooth composite function generated by the objective and the single valued control state mapping in this paper the control state mapping is much more complicated than in most mpecs solved in the literature so far and the generalization of the relevant results is by no means straightforward numerical examples illustrate the efficiency and reliability of the suggested approach

stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications abstract we consider a class of optimization problems that is called a mathematical program with vanishing constraints mpvc for short this class has some similarities to mathematical programs with equilibrium constraints mpecs for short and typically violates standard constraint qualifications hence the well known karush kuhn tucker conditions do not provide necessary optimality criteria in order to obtain reasonable first order conditions under very weak assumptions we introduce several mpvc tailored constraint qualifications discuss their relation and prove an optimality condition which may be viewed as the counterpart of what is called m stationarity in the mpec field

a relaxed constant positive linear dependence constraint qualification and applications in this work we introduce a relaxed version of the constant positive linear dependence constraint qualification cpld that we call rcpld this development is inspired by a recent generalization of the constant rank constraint qualification by minchenko and stakhovski that was called rcrcq we show that rcpld is enough to ensure the convergence of an augmented lagrangian algorithm and that it asserts the validity of an error bound we also provide proofs and counter examples that show the relations of rcrcq and rcpld with other known constraint qualifications in particular rcpld is strictly weaker than cpld and rcrcq while still stronger than abadie s constraint qualification we also verify that the second order necessary optimality condition holds under rcrcq

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

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 new system of generalized mixed quasi variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of generalized mixed quasi variational inclusions with h monotone operators we prove the convergence of a new iterative algorithm for this system of generalized mixed quasi variational inclusions the results in this paper extend and improve some known results in the literature

a new regularization method for mathematical programs with complementarity constraints with strong convergence properties mathematical programs with equilibrium or complementarity constraints mpecs form a difficult class of optimization problems the feasible set has a very special structure and violates most of the standard constraint qualifications therefore one typically applies specialized algorithms in order to solve mpecs one very prominent class of specialized algorithms are the regularization or relaxation methods the first regularization method for mpecs is due to scholtes siam j optim 11 2001 pp 918 936 but in the meantime there exist a number of different regularization schemes which try to relax the difficult constraints in different ways however almost all regularization methods converge to c stationary points only which is a very weak stationarity concept an exception is a recent method by kadrani dussault and benchakroun siam j optim 20 2009 pp 78 103 whose limit points are shown to be m stationary here we provide a new regularization method which also converges to m sta

dynamic ordered sets with exponential search trees we introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully dynamic linear space data structures this leads to an optimal bound of o slog n log log n for searching and updating a dynamic set x of n integer keys in linear space searching x for an integer y means finding the maximum key in x which is smaller than or equal to y this problem is equivalent to the standard text book problem of maintaining an ordered set the best previous deterministic linear space bound was o log n log log n due to fredman and willard from stoc 1990 no better deterministic search bound was known using polynomial space we also get the following worst case linear space trade offs between the number n the word length w and the maximal key u our results are generalized to finger searching and string searching providing optimal results for both in terms of n

nonlinear relaxed cocoercive variational inclusions involving a η accretive mappings in banach spaces in this paper we introduce a new concept of a h accretive mappings which generalizes the existing monotone or accretive operators we study some properties of a h accretive mappings and define resolvent operators associated with a h accretive mappings by using the new resolvent operator technique we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed cocoercive variational inclusions involving a h accretive mappings and study applications of a h accretive mappings to the approximation solvability of this class of nonlinear relaxed cocoercive variational inclusions in q uniformly smooth banach spaces our results improve and generalize the corresponding results of recent works

power control in networks with heterogeneous users a quasi variational inequality approach this paper deals with the power allocation problem in a multipoint to multipoint network which is heterogenous in the sense that each transmit and receiver pair can arbitrarily choose whether to selfishly maximize its own rate or energy efficiency this is achieved by modeling the transmit and receiver pairs as rational players that engage in a noncooperative game in which the utility function changes according to each player s nature the underlying game is reformulated as a quasi variational inequality qvi problem using convex fractional program theory the equivalence between the qvi and the noncooperative game provides us with all the mathematical tools to study the uniqueness of its nash equilibrium points and to derive novel algorithms that allow the network to converge to these points in an iterative manner both with and without the need for a centralized processing numerical results are used to validate the proposed solutions in different operating conditions

two new weak constraint qualifications and applications we present two new constraint qualifications cqs that are weaker than the recently introduced relaxed constant positive linear dependence rcpld cq rcpld is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally a major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a cq this is done in the first new cq which we call the constant rank of the subspace component crsc cq this new cq also preserves many of the good properties of rcpld such as local stability and the validity of an error bound we also introduce an even weaker cq called the constant positive generator cpg which can replace rcpld in the analysis of the global convergence of algorithms we close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods sequential quadratic programming augmented lagrangians

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

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

convergence and stability of an iterative algorithm for a system of generalized implicit variational like inclusions in banach spaces abstract in this paper we give the notion of m proximal mapping for a nonconvex proper lower semicontinuous and subdifferentiable functional on banach space which is an extension of proximal mappings studied in x p ding f q xia a new class of completely generalized quasi variational inclusions in banach spaces j comput appl math 147 2002 369 383 k r kazmi m i bhat convergence and stability of iterative algorithms of generalized set valued variational like inclusions in banach spaces appl math comput 113 2005 153 165 k r kazmi m i bhat n ahmad an iterative algorithm based on m proximal mappings for a system of generalized implicit variational inclusions in banach spaces j comput appl math 233 2009 361 371 we prove its existence and lipschitz continuity in reflexive banach space further we consider a system of generalized implicit variational like inclusions in banach spaces and show its equivalence with a system of implicit equations using the concept of m proximal mappings using this equivalence we propose a new iterative algorithm for the system of generalized implicit variational like inclusions furthermore we prove the existence of solution of the system of generalized implicit variational like inclusions and discuss the convergence and stability analysis of the iterative algorithm in the setting of uniformly smooth banach spaces

an explicit projection method for a system of nonlinear variational inequalities with different cocoercive mappings in this paper we introduce and consider a new system of variational inequalities involving two different operators using the projection technique we suggest and analyze new explicit iterative methods for this system of variational inequalities we also study the convergence analysis of the new iterative method under certain mild conditions since this new system includes the system of variational inequalities involving the single operator variational inequalities and related optimization problems as special cases results obtained in this paper continue to hold for these problems our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

strongly nonlinear quasivariational inequalities abstract in this paper we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area we also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone

lagrange multipliers and calmness conditions of order p in this paper by assuming that a non lipschitz penalty function is exact new conditions for the existence of lagrange multipliers are established for an inequality and equality constrained continuously differentiable optimization problem this is done by virtue of a first order necessary optimality condition of the penalty problem which is obtained by estimating dini upper directional derivatives of the penalty function in terms of taylor expansions and a farkas lemma relations among the obtained results and some well known constraint qualifications are discussed

a system of generalized variational inclusions involving generalized h accretive mapping in real q uniformly smooth banach spaces abstract in this paper we consider a class of accretive mappings called generalized h accretive mappings in banach spaces we prove that the proximal point mapping of the generalized h accretive mapping is single valued and lipschitz continuous further we consider a system of generalized variational inclusions involving generalized h accretive mappings in real q uniformly smooth banach spaces using proximal point mapping method we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions furthermore we discuss the convergence criteria of the iterative algorithm under some suitable conditions our results can be viewed as a refinement and improvement of some known results in the literature

the zero duality gap property and lower semicontinuity of the perturbation function we examine the validity of the zero duality gap properties for two important dual schemes a generalized augmented lagrangian dual scheme and a nonlinear lagrange type dual scheme the necessary and sufficient conditions for the zero duality gap property to hold are established in terms of the lower semicontinuity of the perturbation functions

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

h η accretive operators with an application for solving set valued variational inclusions in banach spaces in this paper we introduce a new class of accretive operators h h accretive operators which generalize many existing monotone or accretive operators the resolvent operator associated with an h h accretive operator is defined and its lipschitz continuity is presented by using the new resolvent operator technique we also introduce and study a new class of set valued variational inclusions involving h h accretive operators and construct a new algorithm for solving this class of set valued variational inclusions these results are new and improve and generalize many known corresponding results

an iterative algorithm based on m proximal mappings for a system of generalized implicit variational inclusions in banach spaces in this paper we give the notion of m proximal mapping an extension of p proximal mapping given in x p ding f q xia a new class of completely generalized quasi variational inclusions in banach spaces j comput appl math 147 2002 369 383 for a nonconvex proper lower semicontinuous and subdifferentiable functional on banach space and prove its existence and lipschitz continuity further we consider a system of generalized implicit variational inclusions in banach spaces and show its equivalence with a system of implicit wiener hopf equations using the concept of m proximal mappings using this equivalence we propose a new iterative algorithm for the system of generalized implicit variational inclusions furthermore we prove the existence of solution of the system of generalized implicit variational inclusions and discuss the convergence and stability analysis of the iterative algorithm

a unified augmented lagrangian approach to duality and exact penalization in this paper the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real valued function are established via a generalized augmented lagrangian and corresponding generalized augmented lagrangian problems in which no convexity is imposed on the augmenting function these results further imply a zero duality gap property between the primal problem and the generalized augmented lagrangian dual problem a necessary and sufficient condition for the exact penalty representation in the framework of a generalized augmented lagrangian is obtained in the context of constrained programs we show that generalized augmented lagrangians present a unified approach to several classes of exact penalization results some equivalences among exact penalization results are obtained

characterizing fj and kkt conditions in nonconvex mathematical programming with applications in this paper we analyze the fritz john and karush kuhn tucker kkt conditions for a g teaux differentiable nonconvex optimization problem with inequality constraints and a geometric constraint set the fritz john condition is characterized in terms of an alternative theorem which covers beyond standard situations while characterizations of kkt conditions without assuming constraints qualifications are related to strong duality of a suitable linear approximation of the given problem and the properties of its associated image mapping such characterizations are suitable for dealing with some problems in structural optimization where most of the known constraint qualifications fail in particular several examples are given showing the usefulness and optimality in a certain sense of our results which provide much more information than those including the mordukhovich normal cone or clarke s appearing elsewhere the case with a single inequality constraint is discussed in detail by establishing

a new system of variational inclusions with h η monotone operators in hilbert spaces in this paper we introduce and study a new system of variational inclusions involving h h monotone operators in hilbert space using the resolvent operator associated with h h monotone operators we prove the existence and uniqueness of solutions for this new system of variational inclusions we also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm

strong duality in cone constrained nonconvex optimization in this paper we deepen the analysis of the conditions that ensure strong duality for a cone constrained nonconvex optimization problem we first establish a necessary and sufficient condition for the validity of strong duality without convexity assumptions with a possibly empty solution set of the original problem and second via slater type conditions involving quasi interior or quasirelative interior notions various results about strong duality are also obtained our conditions can be used where no previous result is applicable even in a finite dimensional or convex setting

lipschitz and holder stability of optimization problems and generalized equations this paper studies stability aspects of solutions of parametric mathematical programs and generalized equations respectively with disjunctive constraints we present sufficient conditions that under some constraint qualifications ensuring metric subregularity of the constraint mapping continuity results of upper lipschitz and upper holder type respectively hold furthermore we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate how some classical results for the nonlinear programming problem can be recovered and even improved by our theory

fusion trees can be implemented with ac 0 instructions only addressing a problem of fredman and willard we implement fusion trees in deterministic linear space using ac o instructions only more precisely we show that a subset of 0 2 w 1 of size n

generalized quasi variational like inclusions with nonconvex functionals in this paper two new concepts of h subdifferential and h proximal mappings of a proper functional is introduced in hilbert spaces the existence and lipschitz continuity of h proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of generalized quasi variational like inclusions with a nonconvex functional a new iterative algorithms for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given these algorithm and existence result generalize many known results in the literature

parallel schemes for solving a system of extended general quasi variational inequalities in this paper we consider a new system of extended general quasi variational inequalities involving six nonlinear operators using projection operator technique we show that the system of extended general quasi variational inequalities is equivalent to a system of fixed point problems using this alternative equivalent formulation we propose and analyze some parallel schemes for solving a system of extended general quasi variational inequalities the convergence of these new schemes is discussed under some mild conditions several special cases are discussed results obtained in this paper continue to hold for these problems the ideas and techniques of this paper may stimulate further research in this dynamic field

mathematical programs with vanishing constraints optimality conditions and constraint qualifications we consider a difficult class of optimization problems that we call a mathematical program with vanishing constraints problems of this kind arise in various applications including optimal topology design problems of mechanical structures we show that some standard constraint qualifications like licq and mfcq usually do not hold at a local minimum of our program whereas the abadie constraint qualification is sometimes satisfied we also introduce a suitable modification of the standard abadie constraint qualification as well as a corresponding optimality condition and show that this modified constraint qualification holds under fairly mild assumptions we also discuss the relation between our class of optimization problems with vanishing constraints and a mathematical program with equilibrium constraints

enhanced fritz john conditions for convex programming we consider convex constrained optimization problems and we enhance the classical fritz john optimality conditions to assert the existence of multipliers with special sensitivity properties in particular we prove the existence of fritz john multipliers that are informative in the sense that they identify constraints whose relaxation at rates proportional to the multipliers strictly improves the primal optimal value moreover we show that if the set of geometric multipliers is nonempty then the minimum norm vector of this set is informative and defines the optimal rate of cost improvement per unit constraint violation our assumptions are very general and in particular allow for the presence of a duality gap and the nonexistence of optimal solutions in particular for the case where there is a duality gap we establish enhanced fritz john conditions involving the dual optimal value and dual optimal solutions

stationarity conditions and constraint qualifications for mathematical programs with switching constraints in optimal control switching structures demanding at most one control to be active at any time instance appear frequently discretizing such problems a so called mathematical program with switching constraints is obtained although these problems are related to other types of disjunctive programs like optimization problems with complementarity or vanishing constraints their inherent structure makes a separate consideration necessary since standard constraint qualifications are likely to fail at the feasible points of switching constrained optimization problems stationarity notions which are weaker than the associated karush kuhn tucker conditions need to be investigated in order to find applicable necessary optimality conditions furthermore appropriately tailored constraint qualifications need to be formulated in this paper we introduce suitable notions of weak mordukhovich and strong stationarity for mathematical programs with switching constraints and present some associated constraint qualifications our findings are exploited to state necessary optimality conditions for discretized optimal control problems with switching constraints furthermore we apply our results to optimization problems with either or constraints first a novel reformulation of such problems using switching constraints is presented second the derived surrogate problem is exploited to obtain necessary optimality conditions for the original program

on a new system of generalized mixed quasi variational like inclusions involving a η m accretive operators with applications in this paper we introduce a new and interesting system of generalized mixed quasi variational like inclusions with a h m accretive operators and relaxed cocoercive mappings which contains variational inequalities variational inclusions systems of variational inequalities systems of variational like inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the a h m accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unifies extends and improves some known results in the literature

dynamic range majority data structures given a set p of n coloured points on the real line we study the problem of answering range majority or heavy hitter queries on p more specifically for a query range q we want to return each colour that is assigned to more than an fraction of the points contained in q we present a new data structure for answering range majority queries on a dynamic set of points where 0 1 our data structure uses o n space supports queries in o lg n time and updates in o lg n amortized time if the coordinates of the points are integers then the query time can be improved to o lg n lg lg n for constant values of this improved query time matches an existing lower bound for any data structure with polylogarithmic update time we also generalize our data structure to handle sets of points in d dimensions for d 2 as well as dynamic arrays in which each entry is a colour

h φ η monotone operators in banach spaces with an application to variational inclusions in this paper we introduce and study a new class of h f email protected operators in banach spaces we define a proximal mapping associated with the h f email protected operator and show its lipschitz continuity as an application we consider the solvability for a class of variational inclusions involving the h f email protected operators in banach spaces by using the technique of proximal mapping an iterative algorithm for solving such class of variational inclusions is constructed in banach spaces under some suitable conditions we prove the convergence of iterative sequence generated by the algorithm

a mixed integer programming for robust truss topology optimization with stress constraints this paper presents a mixed integer programming mip formulation for robust topology optimization of trusses subjected to the stress constraints under the uncertain load a design dependent uncertainty model of the external load is proposed for dealing with the variation of truss topology in the course of optimization for a truss with the discrete member cross sectional areas it is shown that the robust topology optimization problem can be reduced to an mip problem which is solved globally numerical examples illustrate that the robust optimal topology of a truss depends on the magnitude of uncertainty

local stress constrained and slope constrained sand topology optimisation summary we study the alternative simultaneous analysis and design sand formulation of the local stress and slope constrained topology design problem it is demonstrated that a standard trust region lagrange newton sequential quadratic programming sqp type algorithm based in this case on strictly convex and separable approximate subproblems may converge to singular optima of the local stress constrained problem without having to resort to relaxation or perturbation techniques moreover due to the negation of the sensitivity analyses in sand the density and displacement variables are independent and the immense sparsity of the sand problem solutions to large scale problem instances may be obtained in a reasonable amount of computation time this article is protected by copyright all rights reserved

transdichotomous results in computational geometry i point location in sublogarithmic time given a planar subdivision whose coordinates are integers bounded by u leq2 w we present a linear space data structure that can answer point location queries in o min lg n lg lg n sqrt lg u lg lg u time on the unit cost random access machine ram with word size w this is the first result to beat the standard theta lg n bound for infinite precision models as a consequence we obtain the first o n lg n randomized algorithms for many fundamental problems in computational geometry for arbitrary integer input on the word ram including constructing the convex hull of a three dimensional 3d point set computing the voronoi diagram or the euclidean minimum spanning tree of a planar point set triangulating a polygon with holes and finding intersections among a set of line segments higher dimensional extensions and applications are also discussed though computational geometry with bounded precision input has been investigated for a long time improvements have been limited largely to problems of an orthogonal flavor our results surpass this long standing limitation answering for example a question of willard soda 92

the p step iterative algorithm for a system of generalized mixed quasi variational inclusions with a η accretive operators in q uniformly smooth banach spaces in this paper we introduce and study a new system of generalized mixed quasi variational inclusions with a h accretive operators in q uniformly smooth banach spaces by using the resolvent operator technique associated with a h accretive operators we construct a new p step iterative algorithm for solving this system of generalized mixed quasi variational inclusions in real q uniformly smooth banach spaces we also prove the existence of solutions for the generalized mixed quasi variational inclusions and the convergence of iterative sequences generated by algorithm our results improve and generalize many known corresponding results

a new class of variational inclusions with b monotone operators in banach spaces in this paper we introduce and study a new class of variational inclusions in banach spaces for solving such class of variational inclusions we introduce a new notion of b monotone operator and prove the lipschitz continuity of the proximal mapping associated with the b monotone operator by using the proximal mapping an iterative algorithm for solving such class of variational inclusions is constructed in banach spaces under some suitable conditions we prove the convergence of iterative sequence generated by the algorithm

hash functions for priority queues the complexity of priority queue operations is analyzed with respect to the cell probe computational model of a yao j assoc comput mach 28 no 3 1981 615 628 a method utilizing families of hash functions is developed which permits priority queue operations to be implemented in constant worst case time provided that a size constraint is satisfied the minimum necessary size of a family of hash functions for computing the rank function is estimated and contrasted with the minimum size required for perfect hashing

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

iterative approximation of a solution of multi valued variational like inclusion in banach spaces a p η proximal point mapping approach in this paper we introduce a class of p accretive mappings an extension of m accretive mappings c e chidume k r kazmi h zegeye iterative approximation of a solution of a general variational like inclusion in banach spaces int j math math sci 22 2004 1159 1168 and p accretive mappings y p fang n j huang h accretive operators and resolvent operator technique for solving variational inclusions in banach spaces appl math lett 17 2004 647 653 in real banach spaces we prove some properties of p accretive mappings and give the notion of proximal point mapping termed as p proximal point mapping associated with p accretive mapping further using p proximal point mapping technique we prove the existence of solution and discuss the convergence analysis of iterative algorithm for multi valued variational like inclusions in real banach space the theorems presented in this paper extend and improve many known results in the literature

a generalized second order derivative in nonsmooth optimization in this work a new notion of generalized second order directional derivative and generalized hessian for nonsmooth real valued functions is studied the general properties of these mathematical objects are investigated together with some calculus rules that may facilitate their practical computation two applications of these derivatives in optimization theory are considered first to obtaining necessary and sufficient second order optimality conditions for problems with or without constraints and second to extending the newton method for the minimization of a mathcal c 1 1 function

a regularized smoothing newton type algorithm for quasi variational inequalities abstract this paper is concerned with developing an efficient regularized smoothing newton type algorithm for quasi variational inequalities the proposed algorithm takes the advantage of newly introduced smoothing functions and a non monotone line search strategy it is proved to be globally and locally superlinearly quadratically convergent under suitable assumptions numerical results demonstrate that the algorithm generally outperforms the existing interior point method and semismooth method facchinei et al 2014

resolvent operator technique for generalized implicit variational like inclusion in banach space a new class of g accretive mappings is introduced and studied in banach space by using the properties of g accretive mappings the concept of resolvent operators associated with the classical m accretive operators is extended and an iterative algorithm for a new class of generalized implicit variational like inclusion involving g accretive mappings and its convergence results are established in banach space

lagrange multipliers and optimality lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first order optimality conditions formally as a system of equations modern applications with their emphasis on numerical methods and more complicated side conditions than equations have demanded deeper understanding of the concept and how it fits into a larger theoretical picture a major line of research has been the nonsmooth geometry of one sided tangent and normal vectors to the set of points satisfying the given constraints another has been the game theoretic role of multiplier vectors as solutions to a dual problem interpretations as generalized derivatives of the optimal value with respect to problem parameters have also been explored lagrange multipliers are now being seen as arising from a general rule for the subdifferentiation of a nonsmooth objective function which allows black and white constraints to be replaced by penalty expressions this paper traces su

equivalence between priority queues and sorting we present a general deterministic linear space reduction from priority queues to sorting implying that if we can sort up to n keys in s n time per key then there is a priority queue supporting delete and insert in o s n time and find min in constant time conversely a priority queue can trivially be used for sorting first insert all keys to be sorted then extract them in sorted order by repeatedly deleting the minimum asymptotically this settles the complexity of priority queues in terms of that of sorting previously at soda 96 such a result was presented by the author for the special case of monotone priority queues where the minimum is not allowed to decrease besides nailing down the complexity of priority queues to that of sorting and vice versa our result yields several improved bounds for linear space integer priority queues with find min in constant time deterministically we get o log log n update time using a sorting algorithm of han from stoc 02 this improves the o log log n log log log n update time of han from soda 01 randomized we get o slog log n expected update time using a randomized sorting algorithm of han and thorup from focs 02 this improves the o log log n expected update time of thorup from soda 96 deterministically in ac0 without multiplication for any e 0 we get o log log n 1pe update time using an ac0 sorting algorithm of han and thorup from focs 02 this improves the o log log n 2 update time of thorup from soda 98 randomized in ac0 we get o log log n expected update time using a randomized ac0 sorting algorithm of thorup from soda 97 this improves the o log log n 1pe expected update time of thorup also from soda 97 the above bounds assume that each integer is stored in a single word and that word operations take unit time as in the word ram

finding median in read only memory on integer input starting with munro and paterson 1980 13 the selection or median finding problem has been extensively studied in the read only memory model and in streaming models munro and paterson s deterministic algorithm and its subsequent refinements require at least polylogarithmic or logarithmic space whereas the algorithms by munro and raman 1996 14 and raman and ramnath 1999 15 can be made to use just o 1 storage cells but take o n 1 e time for an arbitrarily small constant e 0 in this paper we initiate the first study on this problem when the input is a sequence of integers we show that faster selection algorithms in read only memory are possible if the input is a sequence of integers for example one of our algorithms uses o 1 storage cells and takes o n lg u 1 time where u is the universe size another algorithm uses o 1 storage cells and takes o n lg n lg lg u time a combination of the two yields an algorithm that uses o 1 words of space and takes o n lg 1 n time a bound independent of u we also describe an o n time algorithm for finding an approximate median using o lg e u storage cells all our algorithms are simple and deterministic interestingly one of our algorithms is inspired by centroids of binary trees and finds an approximate median by repeatedly invoking a textbook algorithm for the majority problem this technique could be of independent interest

graph convergence for the h accretive operator in banach spaces with an application abstract in this paper a concept of graph convergence concerned with the h accretive operator is introduced in banach spaces and some equivalence theorems between of graph convergence and resolvent operator convergence for the h accretive operator sequence are proved as an application a perturbed algorithm for solving a class of variational inclusions involving the h accretive operator is constructed under some suitable conditions the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the perturbed algorithm are also given

a generalized hopfield network for nonsmooth constrained convex optimization lie derivative approach this paper proposes a generalized hopfield network for solving general constrained convex optimization problems first the existence and the uniqueness of solutions to the generalized hopfield network in the filippov sense are proved then the lie derivative is introduced to analyze the stability of the network using a differential inclusion the optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced fritz john conditions the convergence rate of the generalized hopfield network can be estimated by the second order derivative of the energy function the effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four tank benchmark

existence of augmented lagrange multipliers reduction to exact penalty functions and localization principle in this article we present new general results on existence of augmented lagrange multipliers we define a penalty function associated with an augmented lagrangian and prove that under a certain growth assumption on the augmenting function an augmented lagrange multiplier exists if and only if this penalty function is exact we also develop a new general approach to the study of augmented lagrange multipliers called the localization principle the localization principle allows one to study the local behaviour of the augmented lagrangian near global optimal solutions of the initial optimization problem in order to prove the existence of augmented lagrange multipliers

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

backward sdes with constrained jumps and quasi variational inequalities we consider a class of backward stochastic differential equations bsdes driven by brownian motion and poisson random measure and subject to constraints on the jump component we prove the existence and uniqueness of the minimal solution for the bsdes by using a penalization approach moreover we show that under mild conditions the minimal solutions to these constrained bsdes can be characterized as the unique viscosity solution of quasi variational inequalities qvis which leads to a probabilistic representation for solutions to qvis such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems as a direct consequence this suggests a numerical scheme for the solution of such qvis via the simulation of the penalized bsdes

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

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

h monotone operator and resolvent operator technique for variational inclusions in this paper we introduce a new class of monotone operators h monotone operators the resolvent operator associated with an h monotone operator is defined and its lipschitz continuity is presented we also introduce and study a new class of variational inclusions involving h monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique

optimality conditions via exact penalty functions in this paper we study kkt optimality conditions for constrained nonlinear programming problems and strong and mordukhovich stationarities for mathematical programs with complementarity constraints using l p penalty functions with 0 leq p leq1 we introduce some optimality indication sets by using contingent derivatives of penalty function terms some characterizations of optimality indication sets are obtained by virtue of the original problem data we show that the kkt optimality condition holds at a feasible point if this point is a local minimizer of some l p penalty function with p belonging to the optimality indication set our result on constrained nonlinear programming includes some existing results from the literature as special cases

on the time transformation of mixed integer optimal control problems using a consistent fixed integer control function nonlinear control systems with instantly changing dynamical behavior can be modeled by introducing an additional control function that is integer valued in contrast to a control function that is allowed to have continuous values the discretization of a mixed integer optimal control problem miocp leads to a non differentiable optimization problem and the non differentiability is caused by the integer values the paper is about a time transformation method that is used to transform a miocp with integer dependent constraints into an ordinary optimal control problem differentiability is achieved by replacing a variable integer control function with a fixed integer control function and a variable time allows to change the sequence of active integer values in contrast to other contributions so called control consistent fixed integer control functions are taken into account here it is shown that these control consistent fixed integer control functions allow a better accuracy in the resulting trajectories in particular in the computed switching times the method is verified on analytical and numerical examples

undirected single source shortest paths with positive integer weights in linear time the single source shortest paths problem sssp is one of the classic problems in algorithmic graph theory given a positively weighted graph g with a source vertex s find the shortest path from s to all other vertices in the graph since 1959 all theoretical developments in sssp for general directed and undirected graphs have been based on dijkstra s algorithm visiting the vertices in order of increasing distance from s thus any implementation of dijkstra s algorithm sorts the vertices according to their distances from s however we do not know how to sort in linear time here a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights the algorithm avoids the sorting bottleneck by building a hierarchical bucketing structure identifying vertex pairs that may be visited in any order

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures

the reciprocal variational approach to the signorini problem with friction approximation results in this paper a new variational formulation of the signorini problem with friction is given in terms of the contact stresses the method corresponds to the direct integral equation approach in classical elastostatic problems first the displacement and mixed problems are briefly described together with some numerical results next the displacements are eliminated by the use of green s function and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived then the resulting approximation procedure is studied and certain convergence results are proved finally some remarks on the signorini problem with coulomb friction are presented numerical results illustrate the theory