‎This paper describes a new optimization method for solving continuous semi-infinite linear problems‎. ‎With regard to the dual properties‎, ‎the problem is presented as a measure theoretical optimization problem‎, ‎in which the existence of the solution is guaranteed‎. ‎Then‎, ‎on the basis of the atomic measure properties‎, ‎a computation method was presented for obtaining the near optimal so...

The aim of this paper is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first and second order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research.

In this paper we study differentiability and semismoothness properties of functions defined as integrals of parameterized functions. We also discuss applications of the developed theory to the problems of shape-preserving interpolation, option pricing and semi-infinite programming.

We study stochastic linear programming games: a class of stochastic cooperative games whose payoffs under any realization of uncertainty are determined by a specially structured linear program. These games can model a variety of settings, including inventory centralization and cooperative network fortification. We focus on the core of these games under an allocation scheme that determines how p...

Generalized semi-infinite optimization problems (GSIP) are considered. The difference between GSIP and standard semi-infinite problems (SIP) is illustrated by examples. By applying the ’Reduction Ansatz’, optimality conditions for GSIP are derived. Numerical methods for solving GSIP are considered in comparison with methods for SIP. From a theoretical and a practical point of view it is investi...