An approach to characterizing ε-solution sets of convex programs

In this paper, we propose an approach to characterizing epsilon-solution sets of convex programs with a given epsilon > 0. The results are divided into two parts. The first one is devoted to establishing the expressions of epsilon-solution sets of a class of convex infinite programs. The representation is given based on the study of relationships among the following three sets: the set of Lagrange multipliers corresponding to a given epsilon-solution, the set of epsilon-solutions of the dual problem corresponding, and the set of epsilon-Kuhn-Tucker vectors associated with the problem in consideration. The second one is devoted to some special cases: the epsilon-solution sets of convex programs that have set constraints and the almost epsilon-solution sets of convex programs that have finite convex constraints. Several examples are given.