Semi-Infinite Programming

1. Front Matter

   Pages i-xvi

   PDF

2. Theory

   1. Front Matter

      Pages 1-1

      PDF

   2. A Comprehensive Survey of Linear Semi-Infinite Optimization Theory

      • Miguel A. Goberna, Marco A. López

      Pages 3-27

   3. On Stability and Deformation in Semi-Infinite Optimization

      • Hubertus Th. Jongen, Jan-J. Rückmann

      Pages 29-67

   4. Regularity and Stability in Nonlinear Semi-Infinite Optimization

      • Diethard Klatte, René Henrion

      Pages 69-102

   5. First and Second Order Optimality Conditions and Perturbation Analysis of Semi-Infinite Programming Problems

      • Alexander Shapiro

      Pages 103-133

3. Numerical Methods

   1. Front Matter

      Pages 135-135

      PDF

   2. Exact Penalty Function Methods for Nonlinear Semi-Infinite Programming

      • Ian D. Coope, Christopher J. Price

      Pages 137-157

   3. Feasible Sequential Quadratic Programming for Finely Discretized Problems from SIP

      • Craig T. Lawrence, André L. Tits

      Pages 159-193

   4. Numerical Methods for Semi-Infinite Programming: A Survey

      • Rembert Reemtsen, Stephan Görner

      Pages 195-275

   5. Connections between Semi-Infinite and Semidefinite Programming

      • Lieven Vandenberghe, Stephen Boyd

      Pages 277-294

4. Applications

   1. Front Matter

      Pages 295-295

      PDF

   2. Reliability Testing and Semi-Infinite Linear Programming

      • İ. Kuban Altinel, Süleyman Özekici

      Pages 297-322

   3. Semi-Infinite Programming in Orthogonal Wavelet Filter Design

      • K. O. Kortanek, Pierre Moulin

      Pages 323-360

   4. The Design of Nonrecursive Digital Filters via Convex Optimization

      • Alexander W. Potchinkov

      Pages 361-387

   5. Semi-Infinite Programming in Control

      • Ekkehard W. Sachs

      Pages 389-411

5. Back Matter

   Pages 413-414

   PDF

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.

• Analysis
• Optimality Conditions
• Optimization Theory
• Signal
• Wavelet
• linear optimization
• numerical methods
• optimization
• programming

• Institute of Mathematics, Brandenburg Technical University of Cottbus, Germany

  Rembert Reemtsen

• Institute of Applied Mathematics, University of Erlangen-Nuremberg, Germany

  Jan-J. Rückmann

Policies and ethics