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

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.