ON SURROGATE DUALITY FOR ROBUST SEMI-INFINITE OPTIMIZATION PROBLEM

Abstract

Abstract. A semi-inflnite optimization problem involving a quasi-convex objective function and inflnitely many convex constraintfunctions with data uncertainty is considered. A surrogate dualitytheorem for the semi-inflnite optimization problem is given undera closed and convex cone constraint qualiflcation. 1. IntroductionOptimization problems in the face of data uncertainty have beentreated by the worst case approach(the robust approach) or the sto-chastic approach. The worst case approach for optimization problems,which has emerged as a powerful deterministic approach for studyingoptimization problems with data uncertainty, associates an uncertainoptimization problem with its robust counterpart. Many researchers[1, 6, 7, 12] have investigated duality theory for linear or convex pro-gramming problems under uncertainty with the worst case approach.On the other hand, recently, many authors [3, 4, 8, 9, 10, 11, 12]investigated surrogate duality for quasiconvex programming. Surrogateduality is used in not only quasi-convex programming but also integerprogramming and the knapsack problem [2, 3, 4, 8, 9, 10]. In particualr,Suzuki, Kuroiwa and Lee [12] proved a surrogate duality theorem for anoptimization problem involving a quasi-convex objective function andflnitely many convex constraint functions with data uncertainty, and a