ε-Properly Efficiency of Multiobjective Semidefinite Programming with Set-Valued Functions

Chun Hong Yuan,Wei Dong Rong

doi:10.1155/2017/5978130

Abstract

In this paper, we study the ε-properly efficiency of multiobjective semidefinite programming with set-valued functions. Firstly, we obtain the scalarization theorems under the condition of the generalized cone-subconvexlikeness. Then, we establish the alternative theorem which contains matrixes and vectors, the ε-Lagrange multiplier theorems, and the ε-proper saddle point theorems of the primal programming under some suitable conditions.

Highlights

Vector optimization with set-valued functions has been used widely in many fields, such as economics and engineering
By combining approximate solutions of vector optimization problems with multiobjective semidefinite programming, ε-properly efficiency of multiobjective semidefinite programming with set-valued functions is discussed in this paper
The rest of the paper is organized as follows: In Section 2, we introduce some notations and definitions used throughout the text

Summary

Introduction

Vector optimization with set-valued functions has been used widely in many fields, such as economics and engineering. Set-valued optimization problem has aroused extensive concerns among the researchers [1,2,3,4,5,6]. Semidefinite programming involves optimization problems with a linear objective function over semidefinite constraints. It shares many interesting properties with linear programming. By combining approximate solutions of vector optimization problems with multiobjective semidefinite programming, ε-properly efficiency of multiobjective semidefinite programming with set-valued functions is discussed in this paper.

Preliminaries

Scalarization Theorems