Optimization Methods and Software, ISSN 1055-6788, 2019, pp. 1 - 16

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2018, Volume 179, Issue 3, pp. 838 - 867

We examine a class of stochastic mirror descent dynamics in the context of monotone variational inequalities (including Nash equilibrium and saddle-point...

Stochastic differential equations | Mathematics | Theory of Computation | Optimization | Mirror descent | Calculus of Variations and Optimal Control; Optimization | 90C25 | 90C47 | Operations Research/Decision Theory | 90C33 | Applications of Mathematics | Engineering, general | Saddle-point problems | Variational inequalities | MATHEMATICS, APPLIED | EQUATIONS | ALGORITHMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LONG-TIME BEHAVIOR | SYSTEMS | FLOWS | OPERATORS | Game theory | Business schools | Differential equations | Dynamic tests | Sequences | Parameters | Saddle points | Inequalities | Brownian movements | Descent | Convergence | Optimization and Control

Stochastic differential equations | Mathematics | Theory of Computation | Optimization | Mirror descent | Calculus of Variations and Optimal Control; Optimization | 90C25 | 90C47 | Operations Research/Decision Theory | 90C33 | Applications of Mathematics | Engineering, general | Saddle-point problems | Variational inequalities | MATHEMATICS, APPLIED | EQUATIONS | ALGORITHMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | LONG-TIME BEHAVIOR | SYSTEMS | FLOWS | OPERATORS | Game theory | Business schools | Differential equations | Dynamic tests | Sequences | Parameters | Saddle points | Inequalities | Brownian movements | Descent | Convergence | Optimization and Control

Journal Article

Optimization, ISSN 0233-1934, 11/2019, Volume 68, Issue 11, pp. 2191 - 2202

This paper considers the symmetric cone complementarity problem. A new projection and contraction method is presented which only requires some projection...

65K05 | convergence analysis | Euclidean Jordan algebra | 90C33 | Symmetric cone | complementarity problem | projection | Iterative methods | Projection

65K05 | convergence analysis | Euclidean Jordan algebra | 90C33 | Symmetric cone | complementarity problem | projection | Iterative methods | Projection

Journal Article

Mathematical Programming, ISSN 0025-5610, 6/2016, Volume 157, Issue 2, pp. 421 - 449

We consider a three-tier architecture for mobile and pervasive computing scenarios, consisting of a local tier of mobile nodes, a middle tier (cloudlets) of...

Theoretical, Mathematical and Computational Physics | Mobile cloud computing | Mathematics | Generalized Nash equilibrium problem | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Distributed algorithm | 68M20 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | Computer science | Cloud computing | Algorithms | Game theory | Analysis | Studies | Wireless communications | Mathematical analysis | Ubiquitous computing | Architecture (computers) | Servers | Mobile computing | Constraining | Mathematical programming

Theoretical, Mathematical and Computational Physics | Mobile cloud computing | Mathematics | Generalized Nash equilibrium problem | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Distributed algorithm | 68M20 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | Computer science | Cloud computing | Algorithms | Game theory | Analysis | Studies | Wireless communications | Mathematical analysis | Ubiquitous computing | Architecture (computers) | Servers | Mobile computing | Constraining | Mathematical programming

Journal Article

Optimization, ISSN 0233-1934, 09/2018, Volume 67, Issue 9, pp. 1377 - 1388

In this paper, a new iterative method for finding the projection onto the intersection of two closed convex sets in the framework of Banach spaces is...

47J20 | 90C33 | 47H09 | variational inequality | projection | 47N10 | Accretive operator | resolvent | 47H06 | strong convergence | WEAK | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPERATORS | FIXED-POINTS | Computational geometry | Iterative algorithms | Convexity | Banach space | Convergence

47J20 | 90C33 | 47H09 | variational inequality | projection | 47N10 | Accretive operator | resolvent | 47H06 | strong convergence | WEAK | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPERATORS | FIXED-POINTS | Computational geometry | Iterative algorithms | Convexity | Banach space | Convergence

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 11/2018, Volume 66, Issue 11, pp. 2156 - 2167

A new error bound for the linear complementarity problem is obtained when the involved matrix is a B-matrix. This bound improves existing results. Finally, two...

Error bound | 65F35 | linear complementarity problem | 90C33 | 60G50 | B-matrix | MATHEMATICS | Mathematical analysis | Matrix methods

Error bound | 65F35 | linear complementarity problem | 90C33 | 60G50 | B-matrix | MATHEMATICS | Mathematical analysis | Matrix methods

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 05/2018, Volume 95, Issue 5, pp. 845 - 869

In this paper, we establish a theoretical framework of infeasible path-following interior point algorithm for Cartesian nonlinear complementarity problems over...

Cartesian | nonlinear complementarity problem | 90C51 | 90C33 | infeasible | symmetric cone | interior point algorithm

Cartesian | nonlinear complementarity problem | 90C51 | 90C33 | infeasible | symmetric cone | interior point algorithm

Journal Article

2006, Nonconvex optimization and its applications, ISBN 9780387329000, Volume 87, xiv, 338

Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics and also has many...

Fixed point theory | Nonlinear operators | Mathematics

Fixed point theory | Nonlinear operators | Mathematics

Book

Journal of Inequalities and Applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1

We consider a kind of nonsmooth optimization problems with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...

Global convergence | Nonsmooth optimization problem | 90C30 | Smoothing modified three-term conjugate gradient method | Research | 90C33

Global convergence | Nonsmooth optimization problem | 90C30 | Smoothing modified three-term conjugate gradient method | Research | 90C33

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2016, Volume 170, Issue 1, pp. 72 - 84

Recently, the tensor complementarity problem has been investigated in the literature. An important question involving the property of global uniqueness and...

Tensor complementarity problem | Mathematics | Theory of Computation | 15A69 | Optimization | Strong P tensor | 15A18 | P tensor | 65F10 | Calculus of Variations and Optimal Control; Optimization | 90C33 | 65K10 | 65F15 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Nonlinear complementarity problem | Global uniqueness and solvability | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | POSITIVE-DEFINITE | Studies | Mathematical analysis | Nonlinear systems | Construction | Tensors | Uniqueness

Tensor complementarity problem | Mathematics | Theory of Computation | 15A69 | Optimization | Strong P tensor | 15A18 | P tensor | 65F10 | Calculus of Variations and Optimal Control; Optimization | 90C33 | 65K10 | 65F15 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Nonlinear complementarity problem | Global uniqueness and solvability | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | POSITIVE-DEFINITE | Studies | Mathematical analysis | Nonlinear systems | Construction | Tensors | Uniqueness

Journal Article

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 12/2018, Volume 179, Issue 3, pp. 820 - 837

This paper focuses on bilevel programs with a convex lower-level problem violating Slater's constraint qualification. We relax the constrained domain of the...

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C30 | Complementarity constraints | Bilevel programs | 90C33 | MATHEMATICAL PROGRAMS | ALGORITHM | Slater's constraint qualification | Nonlinear programs | Lower convergence | OPTIMALITY CONDITIONS | Algorithms

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C30 | Complementarity constraints | Bilevel programs | 90C33 | MATHEMATICAL PROGRAMS | ALGORITHM | Slater's constraint qualification | Nonlinear programs | Lower convergence | OPTIMALITY CONDITIONS | Algorithms

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 09/2019, Volume 67, Issue 9, pp. 1773 - 1784

In this paper, the convergence conditions of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear...

H-splitting | synchronous multisplitting | Linear complementarity problem | two-step modulus-based method | 65F10 | 90C33 | MATHEMATICS | Theorems | Splitting | Mathematical analysis | Matrix methods | Convergence

H-splitting | synchronous multisplitting | Linear complementarity problem | two-step modulus-based method | 65F10 | 90C33 | MATHEMATICS | Theorems | Splitting | Mathematical analysis | Matrix methods | Convergence

Journal Article

Numerical Algorithms, ISSN 1017-1398, 02/2019, Volume 80, Issue 2, pp. 521 - 532

We introduce strong B-matrices and strong B-Nekrasov matrices, for which some error bounds for linear complementarity problems are analyzed. In particular, it...

B-matrices | Error bounds | Linear complementarity problems | B-Nekrasov matrices | P-matrices | 90C31 | 65G50 | MATHEMATICS, APPLIED | 90C33 | MATRICES | 15A48

B-matrices | Error bounds | Linear complementarity problems | B-Nekrasov matrices | P-matrices | 90C31 | 65G50 | MATHEMATICS, APPLIED | 90C33 | MATRICES | 15A48

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 9

Zero point problems of two accretive operators and fixed point problems of a nonexpansive mappings are investigated based on a Mann-like iterative algorithm....

accretive operator | fixed point | Analysis | 90C33 | 47H09 | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | 47H06 | resolvent | MATHEMATICS, APPLIED | INCLUSIONS | FEASIBILITY PROBLEM | SUM | ITERATIVE ALGORITHMS | MATHEMATICS | BANACH-SPACES | ZERO POINTS | MONOTONE-OPERATORS | FIXED-POINT PROBLEMS | Operators | Theorems | Algorithms | Inequalities | Iterative algorithms | Mapping | Banach space | Convergence

accretive operator | fixed point | Analysis | 90C33 | 47H09 | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | 47H06 | resolvent | MATHEMATICS, APPLIED | INCLUSIONS | FEASIBILITY PROBLEM | SUM | ITERATIVE ALGORITHMS | MATHEMATICS | BANACH-SPACES | ZERO POINTS | MONOTONE-OPERATORS | FIXED-POINT PROBLEMS | Operators | Theorems | Algorithms | Inequalities | Iterative algorithms | Mapping | Banach space | Convergence

Journal Article

Mathematical Programming, ISSN 0025-5610, 6/2011, Volume 128, Issue 1, pp. 253 - 283

In this paper, we present several new rank-one decomposition theorems for Hermitian positive semidefinite matrices, which generalize our previous results in...

Joint numerical range | Theoretical, Mathematical and Computational Physics | Mathematics | Matrix rank-one decomposition | 90C05 | Positive semidefinite Hermitian matrix | Mathematical Methods in Physics | 90C51 | Quadratic optimization | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | 90C33 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SUBPROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSTRAINTS | OPTIMIZATION | Radar systems | Mathematical optimization | Studies | Theorems | Matrix | Mathematical analysis | Gold | Construction | Decomposition | Asian | Manuscripts | Optimization | Matlab

Joint numerical range | Theoretical, Mathematical and Computational Physics | Mathematics | Matrix rank-one decomposition | 90C05 | Positive semidefinite Hermitian matrix | Mathematical Methods in Physics | 90C51 | Quadratic optimization | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | 90C33 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SUBPROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSTRAINTS | OPTIMIZATION | Radar systems | Mathematical optimization | Studies | Theorems | Matrix | Mathematical analysis | Gold | Construction | Decomposition | Asian | Manuscripts | Optimization | Matlab

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 04/2019, Volume 67, Issue 4, pp. 685 - 12

Strict feasibility is an important issue in studies on the theory and algorithms of complementarity problems. For the tensor complementarity problem, strict...

tensor complementarity problem | strict feasibility | 65F10 | 90C33 | semi-positive tensor | 65K10 | 65F15 | 15A69 | S-tensor | 15A18 | MATHEMATICS | EIGENVALUES | Tensors | Algorithms | Mathematical analysis | Feasibility studies

tensor complementarity problem | strict feasibility | 65F10 | 90C33 | semi-positive tensor | 65K10 | 65F15 | 15A69 | S-tensor | 15A18 | MATHEMATICS | EIGENVALUES | Tensors | Algorithms | Mathematical analysis | Feasibility studies

Journal Article

Mathematical Programming, ISSN 0025-5610, 4/2014, Volume 144, Issue 1, pp. 369 - 412

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...

Global convergence | KKT conditions | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 90C51 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Quasi-variational inequality | 65K10 | Combinatorics | Interior-point method | FRICTION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | IMPULSE CONTROL | GAMES | FORMULATION | NASH EQUILIBRIUM PROBLEMS | Algorithms | Studies | Analysis | Mathematical programming | Reduction | Viability | Inequalities | Convergence

Global convergence | KKT conditions | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 90C51 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Quasi-variational inequality | 65K10 | Combinatorics | Interior-point method | FRICTION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | IMPULSE CONTROL | GAMES | FORMULATION | NASH EQUILIBRIUM PROBLEMS | Algorithms | Studies | Analysis | Mathematical programming | Reduction | Viability | Inequalities | Convergence

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 9/2019, Volume 75, Issue 1, pp. 177 - 197

In 2016 Aussel, Sultana and Vetrivel developed the concept of projected solution for Nash equilibria. The purpose of this work is to study the same concept of...

Generalized monotonicity | Mathematics | 90C48 | Generalized Nash equilibrium | Optimization | 49J52 | Operations Research/Decision Theory | 49J40 | 90C33 | Quasi-equilibrium problem | Quasi-optimization problem | Quasi-variational inequality | Computer Science, general | Real Functions | Game theory | Economic models | Existence theorems | Equilibrium

Generalized monotonicity | Mathematics | 90C48 | Generalized Nash equilibrium | Optimization | 49J52 | Operations Research/Decision Theory | 49J40 | 90C33 | Quasi-equilibrium problem | Quasi-optimization problem | Quasi-variational inequality | Computer Science, general | Real Functions | Game theory | Economic models | Existence theorems | Equilibrium

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 13

By using the concept of Γ-distance, we prove EVP (Ekeland’s variational principle) on quasi-F-metric (q-F-m) spaces. We apply EVP to get the existence of the...

47H10 | 49J53 | Equilibrium problems | Analysis | 90C33 | Γ -distance | Mathematics, general | Mathematics | Quasi- F -metric space | Applications of Mathematics | Ekeland’s variational principle | 91B50 | Quasi-F-metric space | Γ-distance

47H10 | 49J53 | Equilibrium problems | Analysis | 90C33 | Γ -distance | Mathematics, general | Mathematics | Quasi- F -metric space | Applications of Mathematics | Ekeland’s variational principle | 91B50 | Quasi-F-metric space | Γ-distance

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 13

In this paper, a variant of Mehrotra-type predictor–corrector algorithm is proposed for P∗(κ) $P_{*}(\kappa )$ linear complementarity problems. In this...

Polynomial complexity | 90C51 | P ∗ ( κ ) $P_{}(\kappa )$ linear complementarity problem | Analysis | 90C33 | Mehrotra-type algorithm | Mathematics, general | Mathematics | Applications of Mathematics | Interior point algorithm

Polynomial complexity | 90C51 | P ∗ ( κ ) $P_{}(\kappa )$ linear complementarity problem | Analysis | 90C33 | Mehrotra-type algorithm | Mathematics, general | Mathematics | Applications of Mathematics | Interior point algorithm

Journal Article

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