Semi-Infinite Programming

Semi-infinite programming (briefly: SIP) is an exciting part of mathematical programming. SIP problems include finitely many variables and, in contrast to finite optimization problems, infinitely many inequality constraints. Prob lems of this type naturally arise in approximation theory, optimal control, and at numerous engineering applications where the model contains at least one inequality constraint for each value of a parameter and the parameter, repre senting time, space, frequency etc., varies in a given domain. The treatment of such problems requires particular theoretical and numerical techniques. The theory in SIP as well as the number of numerical SIP methods and appli cations have expanded very fast during the last years. Therefore, the main goal of this monograph is to provide a collection of tutorial and survey type articles which represent a substantial part of the contemporary body of knowledge in SIP. We are glad that leading researchers have contributed to this volume and that their articles are covering a wide range of important topics in this subject. It is our hope that both experienced students and scientists will be well advised to consult this volume. We got the idea for this volume when we were organizing the semi-infinite pro gramming workshop which was held in Cottbus, Germany, in September 1996.

Klappentext

This volume provides an outstanding collection of tutorial and survey articles on semi-infinite programming by leading researchers. While the literature on semi-infinite programming has grown enormously, an up-to-date book on this exciting area of optimization has been sorely lacking. The volume is divided into three parts. The first part, Theory, includes an analysis of sensitivity and stability properties and a discussion of parameter-dependent problems. A comprehensive survey of existing methods and a discussion of connections with semi-definite programming are topics in the second part, Numerical Methods. Investigations of special problems from signal processing, reliability testing, and control theory make up the final part, Applications. Audience: This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering.

Inhalt
1 A Comprehensive Survey of Linear Semi-Infinite Optimization Theory.- 2 On Stability and Deformation in Semi-Infinite Optimization.- 3 Regularity and Stability in Nonlinear Semi-Infinite Optimization.- 4 First and Second Order Optimality Conditions and Perturbation Analysis of Semi-Infinite Programming Problems.- 5 Exact Penalty Function Methods for Nonlinear Semi-Infinite Programming.- 6 Feasible Sequential Quadratic Programming for Finely Discretized Problems from SIP.- 7 Numerical Methods for Semi-Infinite Programming: A Survey.- 8 Connections between Semi-Infinite and Semidefinite Programming.- 9 Reliability Testing and Semi-Infinite Linear Programming.- 10 Semi-Infinite Programming in Orthogonal Wavelet Filter Design.- 11 The Design of Nonrecursive Digital Filters via Convex Optimization.- 12 Semi-Infinite Programming in Control.