Duality for Nonconvex Approximation and Optimization / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
Used and New from Other Sellers
Used and New from Other Sellers
from $30.00
Usually ships in 1-2 business days
(Save 82%)
Other sellers (Hardcover)
  • All (18) from $30.00   
  • New (9) from $52.53   
  • Used (9) from $30.00   


The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

Read More Show Less

Editorial Reviews

From the Publisher

From the reviews:

"Being the first monograph devoted to nonconvex duality, this book is going to become a fundamental source for researchers in the field. An important feature of the book is that it is also accessible to nonspecialists, since, in spite of dealing with a rather specialized topic, it is essentially self-contained. … this monograph is a very useful addition to the existing literature on optimization and approximation and is undoubtedly going to constitute a major reference on nonconvex duality." (Juan-Enrique Martinez-Legaz, Mathematical Reviews, Issue 2006 k)

"This monograph, being the first book of this kind in the literature, covers a wide range of optimization and approximation problems. It provides an excellent overview over the literature and, moreover, it contains a lot of new results and new proofs of known results. The results and the choice of the classes of problems are well motivated. … The monograph is appropriate for graduate students and advanced readers." (Andreas Löhne, Mathematical Methods of Operations Research, Vol. 66, 2007)

"In this monograph the author presents some approaches to duality in nonconvex approximation in normed linear spaces and to duality in nonconvex global optimization in locally convex spaces. … It is my belief that the monograph under review will become a fundamental reference on nonconvex duality for researchers in the field, and, although the topics are very specialized, the monograph is also accessible to nonspecialists … . is strongly recommended to researchers, postgraduate and graduate students interested in nonconvex duality theory." (Fabián Flores Bazán, Zentralblatt MATH, Vol. 1119 (21), 2007)

"This is a nice addition to the literature on nonconvex optimization in locally convex spaces, devoted primarily to nonconvex duality. Most of the material appears for the first time in book form and examples are abundant. … The style is friendly. I strongly recommend this book to graduate students studying nonconvex optimization theory." (Constantin P. Niculescu, Revue Roumaine de Mathématique Pures et Appliquées, Vol. LII (5), 2007)

Read More Show Less

Product Details

  • ISBN-13: 9780387283944
  • Publisher: Springer New York
  • Publication date: 2/16/2006
  • Series: CMS Books in Mathematics Series
  • Edition description: 2006
  • Edition number: 1
  • Pages: 356
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

1 Preliminaries 1
2 Worst approximation 85
3 Duality for quasi-convex supremization 101
4 Optimal solutions for quasi-convex maximization 137
5 Reverse convex best approximation 153
6 Unperturbational duality for reverse convex infimization 169
7 Optimal solutions for reverse convex infimization 203
8 Duality for D.C. optimization problems 213
9 Duality for optimization in the framework of abstract convexity 259
10 Notes and remarks 279
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 & Noble.com 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 & Noble.com 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 & Noble.com 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 BN.com 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 & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com 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 BN.com. 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)