Unified optimality conditions for set-valued optimizations

Geng-Hua Li,Sheng-Jie Li

doi:10.3934/jimo.2018087

Abstract

This paper is devoted to the study of unified optimality conditions for constrained set-valued optimization problems via image space analysis. Necessary and sufficient optimality conditions are given in terms of tangent cones of extended image set. By exploiting such results, we analyse the optimality conditions employing different generalized derivatives.

Highlights

Set-valued optimization is a vital branch of applied mathematics, many optimization problems encountered in economics, engineering and other fields involve vector-valued maps as constraints and objectives
Under appropriate convexity assumptions, we obtain a regular multiplier type sufficient optimality condition involved with the tangent cone of the extended image set
We introduce the definition of minimal points of a set in real normed space Y and the set-valued optimization problem to be studied in this paper

Summary

Introduction

Set-valued optimization is a vital branch of applied mathematics, many optimization problems encountered in economics, engineering and other fields involve vector-valued maps (or set-valued maps) as constraints and objectives (see [1, 13, 16]). Set-valued optimization problem, optimality condition, image space analysis, tangent cone, generalized derivative. By virtue of the tangent cone of the extended image set, we extend the Kurcyusz-Robinson-Zowe regularity assumption and get a generalized Lagrange multiplier type necessary condition of set-valued optimization problems.

Results

Conclusion