Optimization on Metric and Normed Spaces

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Springer, Aug 5, 2010 - Mathematics - 434 pages
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"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.
 

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Contents

1 Introduction
1
2 Exact Penalty in Constrained Optimization
11
3 Stability of the Exact Penalty
81
4 Generic WellPosedness of Minimization Problems
121
5 WellPosedness and Porosity
181
6 Parametric Optimization
225
7 Optimization with Increasing Objective Functions
266
8 Generic WellPosedness of Minimization Problems with Constraints
311
9 Vector Optimization
348
10 Infinite Horizon Problems
395
References
427
Index
432
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