SEMI-INFINITE PROGRAMMING MARCO L OPEZ, GEORG STILL Summary: SEMI-INFINITE PROGRAMMING MARCO L ŽOPEZ, GEORG STILL ABSTRACT. A semi-infinite programming problem is an optimization problem in which finitely many variables appear in infinitely many constraints. This model naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering. The paper, which intends to make a compromise between an introduction and a survey, treats the theoretical basis, numerical methods, applications and historical background of the field. 1. INTRODUCTION 1.1. Problem formulation. A semi-infinite program (SIP) is an optimization problem in finitely many variables x = .x1;:::; xn/ Rn on a feasible set described by infinitely many constraints: (1) P : min x f .x/ s.t. g.x;t/ 0 t T; where T is an infinite index set. For the sake of shortness, we omit additional equality constraints hi.x/ = 0; i = 1;2;:::;m: By F we denote the feasible set of P, whereas v := inf{ f .x/ | x F } is the optimal value, and S := {x F | f .x/ = v} is the optimal set or set of minimizers of the problem. We say that P is feasible or consistent if F = ; and set v = + when F = : With the only ex- Collections: Engineering; Mathematics