Abstract:

This paper is devoted to study the optimality conditions of robust approximate solutions for a convex optimization problem, in which the objective and constraint functions are carried with uncertain data. First of all, under the assumption of a closed convex cone constraint qualification for the constraint functions, the optimality conditions of approximate solutions for the concerned uncertain optimization problem are presented. Then, the concept of robust approximate saddle point is introduced, and the characterization of robust approximate solutions are proposed by saddle points.

Key words: Robust convex optimization, Approximate solution, Approximate optimality condition, Approximate saddle point