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Bi-Level Strategies in Semi-Infinite Programming

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ISBN-10: 1402075677

ISBN-13: 9781402075674

Edition: 2003

Authors: Oliver Stein

List price: $149.99
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Description:

This is the first book that exploits the bi-level structure of semi-infinite programming systematically. It highlights topological and structural aspects of general semi-infinite programming, formulates powerful optimality conditions, which take this structure into account, and gives a conceptually new bi-level solution method. The results are motivated and illustrated by a number of problems from engineering and economics that give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, robust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming. Audience: The book is suitable for graduate…    
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Book details

List price: $149.99
Copyright year: 2003
Publisher: Springer
Publication date: 8/31/2003
Binding: Hardcover
Pages: 202
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.188

List of Symbols
List of Figures
List of Tables
Preface
Acknowledgments
Introduction
Standard semi-infinite programming
General semi-infinite programming
The misconception about the generality of GSIP
Development to a field of active research
Examples and Applications
Chebyshev and reverse Chebyshev approximation
Minimax problems
Robust optimization
Design centering
Defect minimization for operator equations
Disjunctive programming
Topological Structure of the Feasible Set
Abstract index set mappings
A projection formula
A bi-level formula and semi-continuity properties
A set-valued mapping formula
The local structure of M
The completely convex case
Index set mappings with functional constraints
The convex case
The linear case
The C[superscript 1] case
The C[superscript 2] case
Genericity results
Optimality Conditions
Abstract primal optimality conditions
First order approximations of the feasible set
General constraint qualifications
Descriptions of the linearization cones
Degenerate index sets
Dual first order optimality conditions
The standard semi-infinite case
The completely convex case
The convex case
The C[superscript 2] case with Reduction Ansatz
The C[superscript 1] case
Second order optimality conditions
Bi-Level Methods for GSIP
Reformulations of GSIP
The Stackelberg game reformulation of GSIP
The MPEC reformulation of GSIP
A regularization of MPEC by NCP functions
The regularized Stackelberg game
Convergence results for a bi-level method
A parametric reduction lemma
Convergence of global solutions
Convergence of Fritz John points
Quadratic convergence of the optimal values
An outer approximation property
Other bi-level approaches and generalizations
Computational Results
Design centering in two dimensions
Design centering in higher dimensions
Robust optimization
Optimal error bounds for an elliptic operator equation
Final Remarks
References
Index