Semi-Infinite Programming

TL;DR: In this article, a rigorous mathematical formulation for the problem of optimal design under uncertainty is presented, which involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region.

TL;DR: In this article, a mathematical theory for the construction of first order non-differentiable optimization algorithms, related to phase I -phase II methods of feasible directions, is presented. And the applicability of the theory is illustrated with examples that are relevant to engineering design.

TL;DR: Semi-infinite programming (SIP) as discussed by the authors is an optimization problem in which finitely many variables appear in infinitely many constraints, and it naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering.

TL;DR: This paper provides a review of numerical methods for the solution of smooth semi-infinite programming problems and presents fundamental and partly new results on level sets, discretization, and local reduction.