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Topological Aspects of Nonsmooth Optimization [electronic resource] / by Vladimir Shikhman.

By: Shikhman, Vladimir [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Optimization and Its Applications: 64Publisher: New York, NY : Springer New York, 2012Description: XII, 196 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781461418979.Subject(s): Mathematics | Functional analysis | Mathematical optimization | Mathematics | Optimization | Continuous Optimization | Functional AnalysisDDC classification: 519.6 Online resources: Click here to access online
Contents:
Preface. -Notation -- Introduction --  Mathematical Programming Problems with Complementarity -- Constraints --  General Semi-infinite Programming Problems -- Mathematical Programming Problems with Vanishing Constraints -- Bilevel Optimization --  Impacts on Nonsmooth Analysis -- Appendix -- Bibliography -- References -- Index.
In: Springer eBooksSummary: This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness.   Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory.
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Preface. -Notation -- Introduction --  Mathematical Programming Problems with Complementarity -- Constraints --  General Semi-infinite Programming Problems -- Mathematical Programming Problems with Vanishing Constraints -- Bilevel Optimization --  Impacts on Nonsmooth Analysis -- Appendix -- Bibliography -- References -- Index.

This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness.   Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory.

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