Asymptotic Cones and Functions in Optimization and Variational Inequalities / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$135.84
Used and New from Other Sellers
Used and New from Other Sellers
from $23.62
Usually ships in 1-2 business days
(Save 86%)
Other sellers (Hardcover)
  • All (11) from $23.62   
  • New (9) from $23.62   
  • Used (2) from $82.99   

Overview

The book will serve as useful reference and self-contained text for researchers and graduate students in the fields of modern optimization theory and nonlinear analysis.
Read More Show Less

Editorial Reviews

From the Publisher
From the reviews:

"The main purpose of this book is to provide a systematic study of asymptotic cones and asymptotic functions in finite dimensional normed spaces. … Every chapter ends with bibliographical notes. … The book is addressed to graduate students at an advanced level and to researchers and practitioners in the fields of optimization theory, nonlinear programming and applied mathematical sciences. ... We recommend this book to all those who are interested in asymptotic analysis and its use." (Constantin Zalinescu, Zentralblatt MATH, Vol. 1017, 2003)

Read More Show Less

Product Details

  • ISBN-13: 9780387955209
  • Publisher: Springer New York
  • Publication date: 10/1/2002
  • Series: Springer Monographs in Mathematics Series
  • Edition description: 2003
  • Edition number: 1
  • Pages: 249
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.63 (d)

Table of Contents

Preface
1 Convex Analysis and Set-Valued Maps: A Review 1
1.1 Convex Sets 1
1.2 Convex Functions 9
1.3 Support Functions 17
1.4 Set-Valued Maps 20
2 Asymptotic Cones and Functions 25
2.1 Definitions of Asymptotic Cones 25
2.2 Dual Characterization of Asymptotic Cones 31
2.3 Closedness Criteria 32
2.4 Continuous Convex Sets 44
2.5 Asymptotic Functions 47
2.6 Differential Calculus at Infinity 60
2.7 Application I: Semidefinite Optimization 66
2.8 Application II: Modeling and Smoothing Optimization Problems 72
3 Existence and Stability in Optimization Problems 81
3.1 Coercive Problems 81
3.2 Weak Coercivity 85
3.3 Asymptotically Level Stable Functions 93
3.4 Existence of Optimal Solutions 96
3.5 Stability for Constrained Problems 100
3.6 Dual Operations and Subdifferential Calculus 107
3.7 Additional Results in the Convex Case 112
3.8 The Feasibility Problem 116
4 Minimizing and Stationary Sequences 119
4.1 Optimality Conditions in Convex Minimization 119
4.2 Asymptotically Well-Behaved Functions 124
4.3 Error Bounds for Convex Inequality Systems 133
4.4 Stationary Sequences in Constrained Minimization 140
5 Duality in Optimization Problems 145
5.1 Perturbational-Conjugate Duality 145
5.2 Fenchel Duality 154
5.3 Lagrangian Duality 157
5.4 Zero Duality Gap for Special Convex Programs 162
5.5 Duality and Asymptotic Functions 166
5.6 Lagrangians and Minimax Theory 170
5.7 Duality and Stationary Sequences 178
6 Maximal Monotone Maps and Variational Inequalities 183
6.1 Maximal Monotone Maps 183
6.2 Minty Theorem 186
6.3 Convex Functionals and Maximal Monotonicity 191
6.4 Domains and Ranges of Maximal Monotone Maps 195
6.5 Asymptotic Functionals of Maximal Monotone Maps 197
6.6 Further Properties of Maximal Monotone Maps 206
6.7 Variational Inequalities Problems 212
6.8 Existence Results for Variational Inequalities 214
6.9 Duality for Variational Inequalities 221
References 233
Index of Notation 243
Index 245
Read More Show Less

Customer Reviews

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

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

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

Reminder:

  • - 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)