new perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi variational inclusions this paper introduces a new system of extended generalized nonlinear mixed quasi variational inclusions involving a maximal m relaxed h accretive so called a h accretive lan et al 2006 37 mappings in q uniformly smooth banach spaces by using the resolvent operator technique for a maximal m relaxed h accretive mappings due to lan et al we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi variational inclusions and construct a new perturbed n step iterative algorithm with mixed errors for solving the mentioned system we also prove the convergence of the sequences generated by our algorithms in q uniformly smooth banach spaces the results presented in this paper extend and improve some known results in the literature

centrally stable algebras abstract we define an algebra a to be centrally stable if for every epimorphism from a to another algebra b the center z b of b is equal to z a the image of the center of a after providing some examples and basic observations we consider in somewhat greater detail central stability in tensor products of algebras and finally establish our main result which states that a finite dimensional unital algebra a over a perfect field f is centrally stable if and only if a is isomorphic to a direct product of algebras of the form c i f i a i where f i is a field extension of f c i is a commutative f i algebra and a i is a central simple f i algebra

three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

a new method for a class of linear variational inequalities in this paper we introduce a new iterative scheme for the numerical solution of a class of linear variational inequalities each iteration of the method consists essentially only of a projection to a closed convex set and two matrix vector multiplications both the method and the convergence proof are very simple

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

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

a class of gap functions for variational inequalities recently auchmuty 1989 has introduced a new class of merit functions or optimization formulations for variational inequalities in finite dimensional space we develop and generalize auchmuty s results and relate his class of merit functions to other works done in this field especially we investigate differentiability and convexity properties and present characterizations of the set of solutions to variational inequalities we then present new descent algorithms for variational inequalities within this framework including approximate solutions of the direction finding and line search problems the new class of merit functions include the primal and dual gap functions introduced by zuhovickii et al 1969a 1969b and the differentiable merit function recently presented by fukushima 1992 also the descent algorithm proposed by fukushima is a special case from the class of descent methods developed in this paper through a generalization of auchmuty s class of merit functions we extend those inherent in the works of dafermos 1983 cohen 1988 and wu et al 1991 new algorithmic equivalence results relating these algorithm classes to each other and to auchmuty s framework are also given

the extragradient method for finding a common solution of a finite family of variational inequalities and a finite family of fixed point problems in the presence of computational errors abstract in a hilbert space we study the convergence of the subgradient method to a common solution of a finite family of variational inequalities and of a finite family of fixed point problems under the presence of computational errors most results known in the literature establish the convergence of algorithms when computational errors are summable in the present paper the convergence of the subgradient method is established for nonsummable computational errors we show that the subgradient method generates a good approximate solution if the sequence of computational errors is bounded from above by a constant

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

further applications of a splitting algorithm to decomposition in variational inequalities and convex programming a classical method for solving the variational inequality problem is the projection algorithm we show that existing convergence results for this algorithm follow from one given by gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators moreover we extend the projection algorithm to solveany monotone affine variational inequality problem when applied to linear complementarity problems we obtain a matrix splitting algorithm that is simple and for linear quadratic programs massively parallelizable unlike existing matrix splitting algorithms this algorithm converges under no additional assumption on the problem when applied to generalized linear quadratic programs we obtain a decomposition method that unlike existing decomposition methods can simultaneously dualize the linear constraints and diagonalize the cost function this method gives rise to highly parallelizable algorithms for solving a problem of deterministic control in discrete time and for computing the orthogonal projection onto the intersection of convex sets

an iterative scheme for variational inequalities in this paper we introduce and study a general iterative scheme for the numerical solution of finite dimensional variational inequalities this iterative scheme not only contains as special cases the projection linear approximation and relaxation methods but also induces new algorithms then we show that under appropriate assumptions the proposed iterative scheme converges by establishing contraction estimates involving a sequence of norms in en induced by symmetric positive definite matrices gm thus in contrast to the above mentioned methods this technique allows the possibility of adjusting the norm at each step of the algorithm this flexibility will generally yield convergence under weaker assumptions

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

asymptotic convergence analysis of the forward backward splitting algorithm the asymptotic convergence of the forward backward splitting algorithm for solving equations of type 0 t z is analyzed where t is a multivalued maximal monotone operator in the n dimensional euclidean space when the problem has a nonempty solution set and t is split in the form t h with being maximal monotone and h being co coercive with modulus greater than convergence rates are shown under mild conditions to be linear superlinear or sublinear depending on how rapidly 1 and h 1 grow in the neighborhoods of certain specific points as a special case when both and h are polyhedral functions we get r linear convergence and 2 step q linear convergence without any further assumptions on the strict monotonicity on t or on the uniqueness of the solution as another special case when h 0 the splitting algorithm reduces to the proximal point algorithm and we get new results which complement r t rockafellar s and f j luque s earlier results on the proximal point algorithm

a new projection method for variational inequality problems we propose a new projection algorithm for solving the variational inequality problem where the underlying function is continuous and satisfies a certain generalized monotonicity assumption e g it can be pseudomonotone the method is simple and admits a nice geometric interpretation it consists of two steps first we construct an appropriate hyperplane which strictly separates the current iterate from the solutions of the problem this procedure requires a single projection onto the feasible set and employs an armijo type linesearch along a feasible direction then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the halfspace containing the solution set thus in contrast with most other projection type methods only two projection operations per iteration are needed the method is shown to be globally convergent to a solution of the variational inequality problem under minimal assumptions preliminary computational experience is also reported

a bayesian method for combining results from several binomial experiments abstract the problem of combining information related to i binomial experiments each having a distinct probability of success i is considered instead of using a standard exchangeable prior for 1 i we propose a more flexible distribution that takes into account various degrees of similarity among the i s using ideas developed by malec and sedransk we consider a partition g of the experiments and take the i s belonging to the same partition subset to be exchangeable and the i s belonging to distinct subsets to be independent next we perform bayesian inference on conditional on g of course one is typically uncertain about which partition to use and so a prior distribution is assigned on a set of plausible partitions g the final inference on is obtained by combining the conditional inferences according to the posterior distribution of g the methodology adopted in this article offers a wide flexibility in structuring the dependence among the i s this allows the

equilibrium programming the path following approach and dynamics a general formulation of equilibrium is introduced which subsumes a large range of equilibrium models in economics mathematical programming game theory networks organizations etc the existence of a solution is proved by path following and without invocation of a fixed point theorem the path following procedure provides new means for establishing existence of equilibria for constructing them and for interpreting them a dynamic equilibrium model is also presented and the existence stability and computation of dynamic equilibrium paths are discussed moreover these paths can often be interpreted as adjustment processes

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

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

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

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

modelling categorical covariates in bayesian disease mapping by partition structures we consider the problem of mapping the risk from a disease using a series of regional counts of observed and expected cases and information on potential risk factors to analyse this problem from a bayesian viewpoint we propose a methodology which extends a spatial partition model by including categorical covariate information such an extension allows detection of clusters in the residual variation reflecting further possibly unobserved covariates the methodology is implemented by means of reversible jump markov chain monte carlo sampling an application is presented in order to illustrate and compare our proposed extensions with a purely spatial partition model here we analyse a well known data set on lip cancer incidence in scotland

a unified description of iterative algorithms for traffic equilibria the purpose of this paper is to provide a unified description of iterative algorithms for the solution of traffic equilibrium problems we demonstrate that a large number of well known solution techniques can be described in a unified manner through the concept of partial linearization and establish close relationships with other algorithmic classes for nonlinear programming and variational inequalities in the case of nonseparable travel costs the class of partial linearization algorithms are shown to yield new results in the theory of finite dimensional variational inequalities the possibility of applying truncated algorithms within the framework is also discussed

decomposition through formalization in a product space when an optimization problem is posed in a product space it is classical to decompose this problem the goal of this paper is to show how such an approach can be used when the problem to be solved is not naturally posed in a product space by associating systematically to this problem an equivalent one posed in ann fold cartesian product space we obtain by decomposition of the latter both a splitting of operators and a desintegration of constraints for the former applications to three rather classical mathematical programming problems are given

a hybrid method for the solution of some multi commodity spatial equilibrium problems this paper describes a hybrid method for solving the multi commodity transportation and transshipment spatial equilibrium models the method is basically a specialization of the block successive overrelaxation method for solving a linear complementarity problem with certain block structure and consists of solving a sequence of subproblems of the single commodity type these subproblems are solved by a special purpose principal pivoting algorithm developed in an earlier paper under some mild conditions convergence of the proposed method is established finally computational experience of solving some fairly large randomly generated problems by the proposed hybrid method is presented

disequilibrium and variational inequalities in this paper we introduce a new market disequilibrium model in a spatial economic setting which genemlizes a recent spatial disequilibrium model to the asymmetric case we derive two alternative variational inequality formulations of the market conditions in the case of price rigidities and or controls and discuss existence and uniqueness properties we then propose a decomposition algorithm which resolves the variational inequality problem into three distinct and simpler variational inequality subproblems with special structure which are then solved in sequential fashion any appropriate algorithm can then be used to solve the individual subproblems the first variational inequality subproblem however is identical to the one governing the well known spatial price e tilibritmt problem and hence a plethora of algorithms are available for its solution we conclude with computa tional experience with the decomposition algorithm on large scale market examples this work bridges the study of disequilibrium and equilibrium problems via the theory of variational inequalities kepor disequilibrium spatial equilibrium economics variational inequalities