RADIUS OF THE PERTURBATION OF THE OBJECTIVE FUNCTION PRESERVES THE KKT CONDITION IN CONVEX OPTIMIZATION

KOKI  ISHIBASHI; DAISHI  KUROIWA

RADIUS OF THE PERTURBATION OF THE OBJECTIVE FUNCTION PRESERVES THE KKT CONDITION IN CONVEX OPTIMIZATION

Authors

KOKI ISHIBASHI Graduate School of Natural Science and Technology, Shimane University, Japan
DAISHI KUROIWA Department of Mathematical Science, Shimane University, Japan

Keywords:

convex optimization problem, KKT optimality condition, the basic constraint qualification, extreme direction

Abstract

The problem to find the maximum radius of the perturbation of the objective function which preserves the KKT condition at a feasible point is studied. The maximum radius of the problem is described, and certain values concerned with the extreme direction of a positive polar cone of the union of the subdifferentials of the active constraint functions at the point are observed.