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＜電子ブック＞
Topological Aspects of Nonsmooth Optimization / by Vladimir Shikhman
(Nonconvex Optimization and Its Applications ; 64)

版	1st ed. 2012.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2012
本文言語	英語
大きさ	XII, 196 p : online resource
著者標目	*Shikhman, Vladimir author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Functional analysis FREE:Optimization FREE:Continuous Optimization FREE:Functional Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-1-4614-1897-9

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