The paper concerns the study of new classes of parametric optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain, among other constraints, infinitely many of inequality constraints. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We foc...

This note establishes a limiting formula for the conic Lagrangian dual of convex infinite optimization problem, correcting classical version Karney [Math. Programming 27 (1983) 75-82] semi-infinite programs. A reformulation problem with single constraint leads to corresponding dual, called sup-dual, and also primal in case when strong Slater condition holds, which entails sup-duality.

Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And methods use loose over-approximation of uncertainties, leading to conservative controls. To address these challenges, we propose a control-limits aware framework bounded state-de...

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.

This paper deals with the characterization of the sums of compact convex sets with linear subspaces, simplices, sandwiches (convex hulls of pairs of parallel affine manifolds) and parallelotopes in terms of the so-called internal and conical representations, topological and geometrical properties. In particular, it is shown that a closed convex set is a sandwich if and only if its relative boun...