An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems

Abstract

In this paper, the exact minimax penalty function method is applied to solve constrained multiobjective optimization problems involving locally Lipschitz functions. The criteria for a saddle point for the original vector optimization problem are studied with the help of the penalized unconstrained vector optimization problem. Furthermore, we determine the conditions for which the (weak) efficient solutions of the vector optimization problem are equivalent to those of the associated, penalized unconstrained vector optimization problem. Some examples of nonsmooth multiobjective problems solved by using the exact minimax penalty method are presented to illustrate the results established in the paper.