Eléments d'analyse convexe et variationnelle / Dominique Azé

Auteur: Azé, Dominique - AuteurType de document: Monographie Collection: Mathématiques pour le 2ème cycle Langue: françaisPays: FranceÉditeur: Paris : Ellipses, 1997Description: 1 vol. (IX-230 p.) ; 26 cm ISBN: 2729897518 ; br. Note: This volume is a textbook on convex analysis and otimization theory, mainly devoted to undergraduate students, but it can be interesting and useful also for PhD curricula. It is divided into six chapters which contain the main elements of: functional analysis, Sobolev spaces, convex functions, duality theory, convex otimization, and boundary value problems. An appendix is devoted to Lipschitzian functions. Both, classical theorems and more recent and advanced results are included, with all the proofs. The author combines a plain, didactical style with a deep, rigorous mathematical treatment. A list of exercises is proposed at the end of each chapter, with a marker which indicates the difficulty. The complete solutions of all the 60 exercises are given with details, successively. Frequent references and remarks (highlighted within the text) makes the book self-contained. The book is equipped with a useful list of notations and an analytic index. A list of suggested references for deeper investigations and applications is proposed in the bibliography. (Zentralblatt)Bibliographie: Bibliogr. p. [227]-228. Index. Sujets MSC: 49-01 Calculus of variations and optimal control; optimization -- Instructional exposition (textbooks, tutorial papers, etc.)
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This volume is a textbook on convex analysis and otimization theory, mainly devoted to undergraduate students, but it can be interesting and useful also for PhD curricula. It is divided into six chapters which contain the main elements of: functional analysis, Sobolev spaces, convex functions, duality theory, convex otimization, and boundary value problems. An appendix is devoted to Lipschitzian functions. Both, classical theorems and more recent and advanced results are included, with all the proofs. The author combines a plain, didactical style with a deep, rigorous mathematical treatment. A list of exercises is proposed at the end of each chapter, with a marker which indicates the difficulty. The complete solutions of all the 60 exercises are given with details, successively. Frequent references and remarks (highlighted within the text) makes the book self-contained. The book is equipped with a useful list of notations and an analytic index. A list of suggested references for deeper investigations and applications is proposed in the bibliography. (Zentralblatt)

Bibliogr. p. [227]-228. Index

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