Foundations of Optimization

  • Osman Güler

Part of the Graduate Texts in Mathematics book series (GTM, volume 258)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Osman Güler
    Pages 1-29
  3. Osman Güler
    Pages 31-60
  4. Osman Güler
    Pages 61-83
  5. Osman Güler
    Pages 85-115
  6. Osman Güler
    Pages 117-139
  7. Osman Güler
    Pages 141-173
  8. Osman Güler
    Pages 175-193
  9. Osman Güler
    Pages 195-205
  10. Osman Güler
    Pages 209-250
  11. Osman Güler
    Pages 251-273
  12. Osman Güler
    Pages 275-312
  13. Osman Güler
    Pages 313-334
  14. Osman Güler
    Pages 335-360
  15. Osman Güler
    Pages 361-405
  16. Back Matter
    Pages 407-439

About this book

Introduction

The book gives a detailed and rigorous treatment of the theory of optimization (unconstrained optimization, nonlinear programming, semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality in nonlinear programming and the theories of linear inequalities, convex polyhedra, and linear programming are covered in detail. Over two hundred, carefully selected exercises should help the students master the material of the book and give further insight. Some of the most basic results are proved in several independent ways in order to give flexibility to the instructor. A separate chapter gives extensive treatments of three of the most basic optimization algorithms (the steepest-descent method, Newton’s method, the conjugate-gradient method). The first chapter of the book introduces the necessary differential calculus tools used in the book. Several chapters contain more advanced topics in optimization such as Ekeland’s epsilon-variational principle, a deep and detailed study of separation properties of two or more convex sets in general vector spaces, Helly’s theorem and its applications to optimization, etc. The book is suitable as a textbook for a first or second course in optimization at the graduate level. It is also suitable for self-study or as a reference book for advanced readers. The book grew out of author’s experience in teaching a graduate level one-semester course a dozen times since 1993. Osman Guler is a Professor in the Department of Mathematics and Statistics at University of Maryland, Baltimore County. His research interests include mathematical programming, convex analysis, complexity of optimization problems, and operations research.

Keywords

Ekeland’s epsilon-variational principle Newton's method Operations Research algorithms convex polyhedra convexity duality linear optimization linear programming mathematical programming nonlinear analysis nonlinear optimization optimality conditions optimization semi-infinite programming

Authors and affiliations

  • Osman Güler
    • 1
  1. 1.Dept. Mathematics & StatisticsUniversity of Maryland, Baltimore CountyBaltimoreUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-68407-9
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-34431-7
  • Online ISBN 978-0-387-68407-9
  • Series Print ISSN 0072-5285
  • About this book