Bi-Level Strategies in Semi-Infinite Programming

1. Front Matter

   Pages I-XXVII

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2. Introduction

   • Oliver Stein

   Pages 1-10

3. Examples and Applications

   • Oliver Stein

   Pages 11-23

4. Topological Structure of the Feasible Set

   • Oliver Stein

   Pages 25-83

5. Optimality Conditions

   • Oliver Stein

   Pages 85-144

6. Bi-Level Methods for Semi-Infinite Programming

   • Oliver Stein

   Pages 145-169

7. Computational Results

   • Oliver Stein

   Pages 171-185

8. Final Remarks

   • Oliver Stein

   Pages 187-189

9. Back Matter

   Pages 191-202

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Semi-infinite optimization is a vivid field of active research. Recently semi­ infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be­ gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro­ bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.

• Approximation
• Grad
• operations research
• optimization

From the reviews:

"This is the first book which exploits the bilevel structure of semi-infinite programming systematically. It highlights topological and structural aspects of general semi-infinite programming, formulates powerful optimality conditions, and gives a conceptually new bilevel solution method. The book is addressed to graduate students and researchers who work in the fields of optimization and operations research." (Oliver Stein, Zentralblatt MATH, Vol. 1103 (5), 2007)

• Department of Mathematics, Aachen University, Germany

  Oliver Stein

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