ε-optimality criteria for convex programming problems via exact penalty functions

Abstract

In this paper, we presentε-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of anε-solution for the dual problem.