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Titlebook: Calculus Without Derivatives; Jean-Paul Penot Textbook 2013 Springer Science+Business Media New York 2013 Clarke subdifferential.Newton Me

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发表于 2025-3-21 19:59:16 | 显示全部楼层 |阅读模式
书目名称Calculus Without Derivatives
编辑Jean-Paul Penot
视频video
概述Includes all necessary preliminary material.Introduces fundamental aspects of nonsmooth analysis that impact many applications.Presents a balanced picture of the most elementary attempts to replace a
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Calculus Without Derivatives;  Jean-Paul Penot Textbook 2013 Springer Science+Business Media New York 2013 Clarke subdifferential.Newton Me
描述.Calculus Without Derivatives. expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems.  Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories.  .In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed.  The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis..
出版日期Textbook 2013
关键词Clarke subdifferential; Newton Method; approximation; calculus of variations; coderivative; convex analys
版次1
doihttps://doi.org/10.1007/978-1-4614-4538-8
isbn_softcover978-1-4899-8942-0
isbn_ebook978-1-4614-4538-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 2013
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Elementary and Viscosity Subdifferentials,otions are nonconvex, while a dual object exhibits convexity properties. On the other hand, the passages from analytical notions to geometrical notions and the reverse passages are multiple and useful. These connections are part of the attractiveness of nonsmooth analysis.
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Limiting Subdifferentials, Sect. 6.6, we give some attention to a limiting procedure involving directional subdifferentials. Such a construction is particularly adapted to the wide class of weakly compactly generated (WCG) spaces that encompasses separable spaces and reflexive spaces.
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