Approximate Optimality Conditions and Approximate Duality Conditions for Robust Multiobjective Optimization Problems

Thanatchaporn Sirichunwijit, Rabian Wangkeeree

Abstract

In this paper, following robust optimization framework, we consider approximate robust optimal solutions for a nonsmooth multi objective optimization problem with uncertainty of data. Some necessary and sufficient conditions are investigated proving different result for approximate optimal solutions depending on Fritz-John type. The concept of generalized convexity is defined, and the relationship with sufficient optimality theorem. Moreover, by using robust optimization approach(worst-case approach), we establish optimality theorems and duality theorem for two robust approximate optimal solutions of an uncertain multi-objective optimization.