Boris S. Mordukhovich

eBook, PDF

Variational Analysis and Generalized Differentiation II (eBook, PDF)

Applications

Beschreibung

This monograph in two volumes contains a comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces and presents numerous applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first volume is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume describes various applications. Both volumes include abundant bibliographies and extensive commentaries.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 3.73MB

Barrierefreiheit

• Text-to-Speech

Autor

Ph.D. in Mathematics (1973); distinguished faculty and lifetime scholar of the Academy of Scholars; more than 200 publications (including books and patents); many outstanding research and teaching awards; numerous invited talks to various meetings (e.g., 15 keynote presentations during the last year); organizer of conference, special sessions, and issues of journals; Editorial Boards of 11 international journals; grants and awards from NSF, NATO, NSERC, BSF, Australian Research Council, etc.

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 610
• Erscheinungstermin: 2. März 2006
• Englisch
• ISBN-13: 9783540312468
• Artikelnr.: 37368046

Rezensionen

From the reviews:

"The combination of the two volumes provide a thorough, self-contained, well-motivated view of an important line of research in variational analysis. This is a reference text which readers having an interest in variational analysis or any of the application areas should find to be a very useful resource." (Adam B. Levy, SIAM Review, Vol. 48 (3), 2006)

"This two-volume book is a deep and wide treatise on variational analysis and its relationships with several fields of mathematics ... . Among several aspects which make the book beautiful and interesting, there is the fact that the reader is met at a classical level of mathematical analysis ... . it is precious for all scholars who want to learn modern

variational analysis and related fields; indeed, this is a fundamental tool for those who are involved in the applications of mathematics." (Franco Giannessi, Journal of Optimization Theory and Applications, Vol. 131 (2), 2006)

"This ... monograph reflects the abiding and enthusiastic interest of the author in variational analysis. ... Besides mathematics, there are extensive commentaries on the history and genesis of major topics under consideration ... open problems, and an extensive bibliography (1379 references). These features make the book appreciated by students and experts in the field. The book will definitely serve as a fundamental read and also a useful reference. It is highly recommended to all libraries and researchers in the area of variational analysis and optimization." (Panos Pardalos, Journal of Global Optimization, Vol. 36, 2006)

"The new two-volume monograph by B.S. Mordukhovich contains a comprehensive presentation of ... calculus together with numerous applications and extensive commentaries. ... The second volume dedicated to applications, keeps the pace with the first volume as regards the systematic and rigorous exposition and high theoretical level. ... this outstanding work contains aconsiderable number of previously unpublished results. We believe that its both volumes will soon become an indispensable part of the library of each researcher interested in the fields listed above." (Jirí V. Outrata and Michal Cervinka, Mathematical Methods of Operations Research, Vol. 65 (1), 2007)

"The book under review offers an original and powerful way to understand the behavior of sets and functions which are neither smooth nor convex. ... The author includes an extensive bibliography of 1379 references ... . The book is well written in a self-contained way, in the sense that most topics are developed from their beginnings. ... Thus the book should prove to be, for beginners and specialists, a key reference for variational or nonsmooth analysis in both finite-dimensional spaces and infinite-dimensional Asplund spaces." (Lionel Thibault, Mathematical Reviews, Issue 2007 b)

"The author succeeded to place at our disposal a comprehensive and deep insight into a fruitful and continuously developing area in mathematics. He presented the theory of modern variational analysis and generalized differentiation in its full generality. This allowed to cover a large range of applications. We appreciate that the book synthetize a life time work of an important mathematician, and warmly recommend it to specialists in mathematical analysis, differential equations or mathematical economics." (Mihai Pascu, Revue Roumaine de Mathématique Pures et Appliquées, Vol. LII (5), 2007)

"The present monograph provides a comprehensive theory of generalized differentiation and its applications in infinite dimensions. ... Each chapter ... is complemented by historic and bibliographic remarks which are based on an impressive list of references and which allow to put parallel developments in nonsmooth analysis into a context with the author's work. ... will become a fundamental reference in variational analysis and that they will stimulate a lot of fruitfulapplications in the abundance of problems where nonsmoothness is an inherent issue." (René Henrion, Operations Research Letters, Vol. 35 (4), July, 2007)

Aus den Rezensionen: "... Jedes Kapitel wird ... durch einen Abschnitt mit Kommentaren ergänzt. ... Insgesamt enthält das Buch eine Fülle von Material, der allergrößte Teil ... mit dem ... Werk erstmals in Form einer Monographie. ... Wer ... Voraussetzungen mitbringt, wird das ... Buch mit großem Gewinn lesen und ... in ein sehr aktuelles und forschungsintensives Gebiet der Mathematik eingeführt und auf den neuesten Stand gebracht. Das Buch erscheint ... in der renommierten Springer-Reihe ... und dürfte für ... Jahrzehnte, zu einem Standard- und Referenzwerk im Bereich der nichtglatten Analysis und ihren Anwendungen werden." (Ch. Kanzow, in: JB - Jahresbericht der Deutschen Mathematischen Vereinigung, 2008, Vol. 110, Issue 4, S. 46 ff.)