Variational Inequalities and Vector Optimization 2014

Xian-Jun Long,Jian-Wen Peng,Nan-Jing Huang,Jen-Chih Yao

doi:10.1155/2014/214957

Abstract

In the last three decades, the theory of variational analysis provides very effective and powerful techniques for studying a wide class of problems arising in nonlinear equations, optimization problems, economics equilibrium, game theory, complementarity problems, and fixed point problems, as well as other branches of mathematics and engineering sciences. So, the thorough study of both theory and methods about variational inequalities will help us to find new techniques for solving the practical problem. Vector optimization problems have received much attention by many authors due to their extensive applications in many fields such as biology, economics, optimal control, and differential inclusions. Because of the importance and active impact of the variational inequality and the vector optimization problem in the nonlinear analysis and optimization, this special issue, focusing on most recent contributions, includes works on variational inequalities, equilibrium problems and nonexpansive mappings, vector optimization problems and generalized convex functions, robust optimization problems, and optimization problems with applications, which are based on a strict international peer review procedure and our original proposal. A brief review of the papers is given under the following four topics.

Highlights

In the last three decades, the theory of variational analysis provides very effective and powerful techniques for studying a wide class of problems arising in nonlinear equations, optimization problems, economics equilibrium, game theory, complementarity problems, and fixed point problems, as well as other branches of mathematics and engineering sciences
Because of the importance and active impact of the variational inequality and the vector optimization problem in the nonlinear analysis and optimization, this special issue, focusing on most recent contributions, includes works on variational inequalities, equilibrium problems and nonexpansive mappings, vector optimization problems and generalized convex functions, robust optimization problems, and optimization problems with applications, which are based on a strict international peer review procedure and our original proposal
Ceng et al.; (iv) “Weak convergence theorems for bregman relatively nonexpansive mappings in Banach spaces” by C

Summary

Introduction

Because of the importance and active impact of the variational inequality and the vector optimization problem in the nonlinear analysis and optimization, this special issue, focusing on most recent contributions, includes works on variational inequalities, equilibrium problems and nonexpansive mappings, vector optimization problems and generalized convex functions, robust optimization problems, and optimization problems with applications, which are based on a strict international peer review procedure and our original proposal. Editorial Variational Inequalities and Vector Optimization 2014 Xian-Jun Long,1 Jian-Wen Peng,2 Nan-Jing Huang,3 and Jen-Chih Yao4 In the last three decades, the theory of variational analysis provides very effective and powerful techniques for studying a wide class of problems arising in nonlinear equations, optimization problems, economics equilibrium, game theory, complementarity problems, and fixed point problems, as well as other branches of mathematics and engineering sciences.

Results

Conclusion