| 書目名稱 | Convexity and Well-Posed Problems | | 編輯 | Roberto Lucchetti | | 視頻video | http://file.papertrans.cn/238/237863/237863.mp4 | | 概述 | Contains a chapter on hypertopologies (only one other book on this topic).Author includes exercises, for use as a graduate text.Over 45 figures are included.Includes supplementary material: | | 叢書名稱 | CMS Books in Mathematics | | 圖書封面 |  | | 描述 | This book deals mainly with the study of convex functions and their behavior from the point of view of stability with respect to perturbations. We shall consider convex functions from the most modern point of view: a function is de?ned to be convex whenever its epigraph, the set of the points lying above the graph, is a convex set. Thus many of its properties can be seen also as properties of a certain convex set related to it. Moreover, we shall consider extended real valued functions, i. e. , functions taking possibly the values?? and +?. The reason for considering the value +? is the powerful device of including the constraint set of a constrained minimum problem into the objective function itself (by rede?ning it as +? outside the constraint set). Except for trivial cases, the minimum value must be taken at a point where the function is not +?, hence at a point in the constraint set. And the value ?? is allowed because useful operations, such as the inf-convolution, can give rise to functions valued?? even when the primitive objects are real valued. Observe that de?ning the objective function to be +? outside the closed constraint set preserves lower semicontinuity, which is th | | 出版日期 | Textbook 2006 | | 關(guān)鍵詞 | Convexity; calculus; derivative; differential equation; functional analysis; game theory; linear optimizat | | 版次 | 1 | | doi | https://doi.org/10.1007/0-387-31082-7 | | isbn_softcover | 978-1-4419-2111-6 | | isbn_ebook | 978-0-387-31082-4Series ISSN 1613-5237 Series E-ISSN 2197-4152 | | issn_series | 1613-5237 | | copyright | Springer-Verlag New York 2006 |
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