Numerical Methods for Solving Semi-infinite Optimization Problems

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. If the infinite index set also depends on the decision variable of optimization, then the problem is called generalized semi-infinite programming problem (GSIP). Chebyshev approximation, reverse Chebyshev approximation, design centering, robust optimizations, the optimal layout of an assembly line, time minimal control and disjunctive optimization are some examples for GSIP problems. This book gives a brief review of numerical methods for solving semi-infinite programming problems and introduces the semi smooth Newton method for solving GSIP problems. Convergence and numerical results shows that the method is a promising numerical method for solution of GSIP problems.