Variational Analysis and Generalized Differentiation II: Applications / Edition 1

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $72.12
Usually ships in 1-2 business days
(Save 44%)
Other sellers (Hardcover)
  • All (7) from $72.12   
  • New (4) from $93.65   
  • Used (3) from $72.12   


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

Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

Read More Show Less

Editorial Reviews

From the Publisher
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 a considerable 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 fruitful applications in the abundance of problems where nonsmoothness is an inherent issue.” (René Henrion, Operations Research Letters, Vol. 35 (4), July, 2007)

Read More Show Less

Product Details

  • ISBN-13: 9783540254386
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 11/12/2012
  • Series: Grundlehren der mathematischen Wissenschaften Series, #331
  • Edition description: 1st ed. 2006. Corr. 2nd printing 2012
  • Edition number: 1
  • Pages: 610
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.44 (d)

Meet the Author

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.

Read More Show Less

Table of Contents

Constrained Optimization and Equilibria: Necessary Optimality Conditions in Nondifferentiable Programming. Mathematical Programs with Equilibrium Constraints. Multiobjective Optimization. Subextremality and Suboptimality at Linear Rate.- Optimal Control of Evolution Systems in Banach Spaces: Optimal Control of Discrete-Time and Continuous-time Evolution Inclusions. Necessary Optimality Conditions for Differential Inclusions without Relaxation. Maximum Principle for Continuous-Time Systems with Smooth Dynamics. Approximate Maximum Principle in Optimal Control.- Optimal Control of Distributed Systems: Optimization of Differential-Algebraic Inclusions with Delays. Neumann Boundary Control of Semilinear Constrained Hyperbolic Equations. Drichelet Boundary Control of Linear Constrained Hyperbolic Equations. Minimax Control of Parabolic Systems with Pointwise State Constraints.- Applications to Economics: Models of Welfare Economics. Second Welfare Theorem for Nonconvex Economics. Nonconvex Economics with Ordered Commodity Spaces. Further Extensions and Public Goods.- References.- Glossary of Notation.- Index of Statements.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)