CONVEX OPTIMIZATION WITHOUT CONVEXITY OF CONSTRAINTS ON NON-NECESSARILY CONVEX SETS AND ITS APPLICATIONS IN CUSTOMER SATISFACTION IN AUTOMOTIVE INDUSTRY

Abstract

In the present paper, some necessary and su?cient optimality conditions for a convex optimization problem over inequality constraints are presented which are not necessarily convex and are based on convex intersection of non-necessarily convex sets. The oriented distance function and a characterization of the normal cone of the feasible set are used to obtain the optimality conditions. In the second part of the paper, a non-linear smooth optimization model for customer satisfaction in automotive industry is introduced. The results of the first part are applied to solve this problem theoretically.