Isolated Calmness Of Solution Maps In Parametric Optimization Problem

During the last few decades, tremendous progress has been achieved toward sensitivity and stability analysis of solutions to the cone programming. It is well-known that isolated calmness of an arbitrary closed multifunction between finite-dimensional spaces at any point of its graph can be fully characterized via the certain form of graphical derivative for the multifunction at this point. Therefore, it is significant to study the graphical derivative of set-valued mapping.This paper is devoted to the study of the isolated calmness for parametric prob-lem of conic programming, we firstly obtain a characterization of graphical deriva-tive of the regular normal cone mapping using the appropriate conditions when the feasible set of parametric optimization problem is nonconvex. Then another expres-sion of graphical derivative of the regular normal cone mapping is derived according to the well-known relationship between the projection and normal cone operators for convex sets. Secondly, when the feasible set is convex, we provides a complete calculation of the graphical derivative of its normal cone mapping. Finally, the sta-bility of KKT system of optimization problem, namely the isolated calmness of the considered solution map S, is gained under the prior results.