Globally proper efficiency of set-valued optimization and vector variational inequality involving the generalized contingent epiderivative

Chen, Wang; Zhou, Zhi-Ang

doi:10.1186/s13660-018-1891-8

Cited by 2 publications

(2 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such properties are crucial to derive necessary optimality conditions for problem (2.2). See [56] for globally proper efficiency results and optimality conditions for generalized vector variational inequalities involving the generalized contingent epiderivative. Besides stability and sensitivity analysis, the well-posedness of problem (2.2) and related problems has been investigated in [83,143].…”

Section: Stability and Sensitivity Analysismentioning

confidence: 99%

Vector variational inequalities and related topics: A survey of theory and applications

2019

Appl. Set-Valued Anal. Optim.

View full text Add to dashboard Cite

In this survey paper, we give a detailed introduction to some of the recent developments in the field of vector variational inequalities and related problems. By giving several examples and presenting the necessary mathematical background and theories, the survey attempts to draw a broad audience and is accessible to students in mathematics and engineering. In doing this, we will study several scalarization methods for vector variational inequalities, which are necessary, sufficient, or both, for the original problem. We further analyze topological and algebraical properties of the solution set. In particular, the existence of solutions is discussed by presenting several existence results. For this purpose, coercivity conditions ensuring, in a certain sense, the boundedness of the data of the vector variational inequality are required. We will further give a precise overview about existence results and techniques, which are known in the literature. Besides that, we analyze a regularization method for non-coercive vector variational inequalities, which consists of approximating solutions of non-coercive problems by a family of regularized vector variational inequalities. After that, we will study relations between vector variational inequalities and multi-objective optimization problems. Motivated by the duality principle in optimization, we also investigate two inverse vector variational inequalities. Furthermore, we consider gap functions for vector variational inequalities, which enable us to study equivalent optimization problems instead. A completely different approach consists of replacing the vector variational inequality by a parametric system or intersection problem. The idea of image space analysis is to study the vector problem in the image space, using one of the previous reformulations. Since vector variational inequalities are ill-posed in general, in the sense that they may either have no solution or multiple solutions, we study stability and sensitivity analysis results. Especially continuity properties of the corresponding solution mapping are investigated. Finally, we give a brief analysis of stochastic vector variational inequalities, generalized problems and numerical methods.

show abstract

Section: Stability and Sensitivity Analysismentioning

confidence: 99%

Vector variational inequalities and related topics: A survey of theory and applications

2019

Appl. Set-Valued Anal. Optim.

View full text Add to dashboard Cite

show abstract

“…As we all know, convexity and generalized convexity play a crucial role in many aspects of mathematical programming including, for example, optimality conditions, duality theorems, saddle points, variational inequalities and characterizations of the solution sets, one can refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In terms of some properties and characterizations of the solution sets, they are very useful for understanding the behavior of solution methods for optimization problems that have multiple optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of the Solution Sets of Generalized Convex Fuzzy Optimization Problem

Chen

Zhou

2019

Open Mathematics

Self Cite

View full text Add to dashboard Cite

This paper provides some new characterizations of the solution sets for non-differentiable generalized convex fuzzy optimization problem. Firstly, we introduce some new generalized convex fuzzy functions and discuss the relationships among them. Secondly, some properties of these new generalized convex fuzzy functions are given. Finally, as applications, some characterizations of the solution sets for non-differentiable generalized convex fuzzy optimization problem are obtained.

show abstract

Globally proper efficiency of set-valued optimization and vector variational inequality involving the generalized contingent epiderivative

Cited by 2 publications

References 32 publications

Vector variational inequalities and related topics: A survey of theory and applications

Vector variational inequalities and related topics: A survey of theory and applications

Characterizations of the Solution Sets of Generalized Convex Fuzzy Optimization Problem

Contact Info

Product

Resources

About