Optimality conditions for interval-valued univex programming

Lifeng Li,Chang Zhou,Jianke Zhang

doi:10.1186/s13660-019-2002-1

Abstract

We introduce concepts of interval-valued univex mappings, consider optimization conditions for interval-valued univex functions for the constrained interval-valued minimization problem, and show examples for the illustration purposes.

Highlights

Convexity and generalized convexity are important in mathematical programming
Followed by [21] and [22], in this paper, we introduce the concept of interval-valued univex mappings, consider optimization conditions for interval-valued univex functions for the constrained interval-valued minimization problem, and show examples for illustration purposes
Example 4.1 shows that the methods given by [6, 33, 36, 37] cannot solve a kind of optimization problems for interval-valued univex mappings

Summary

Introduction

Convexity and generalized convexity are important in mathematical programming. Invex functions, introduced by Hanson [17], are important generalized convex functions and are successfully used in optimization and equilibrium problems. Wu [36] obtained KKT conditions in an optimization problem with an interval-valued objective function using H-derivatives and the concept of weakly differentiable functions. They studied the relationship between the approach presented with other known approaches given by Wu [36] These methods cannot solve a kind of optimization problems with interval-valued objective functions that are not LU-convex but univex. Example 4.1 shows that the methods given by [6, 33, 36, 37] cannot solve a kind of optimization problems for interval-valued univex mappings. Gm(x) are gH-differentiable interval-valued mappings defined on a nonempty open set X ⊆ Rn. we consider the primal problem:.

Further suppose that

Conclusion