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Springer Optimization and Its Applications

Introduction to Continuous Optimization

Authors: Polyak, Roman A.

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  • Numerous exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization
  • Shows what makes the exterior point methods numerically attractive and why
  • Contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role
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eBook 109,99 €
price for Spain (gross)
  • ISBN 978-3-030-68713-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-030-68711-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization.

The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why.  

The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization.  The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described.  Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.

About the authors

Roman Polyak is Emeritus professor of mathematics and operations research at George Mason University and visiting professor at Technion. He is the author/co-author of several monographs, books chapters, and journal papers. His expertise and interests are in linear and nonlinear programming, game theory, and mathematical economics. Dr. Polyak developed Nonlinear Rescaling (NR) theory and methods of constrained optimization.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 109,99 €
price for Spain (gross)
  • ISBN 978-3-030-68713-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-030-68711-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Continuous Optimization
Authors
Series Title
Springer Optimization and Its Applications
Series Volume
172
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-68713-7
DOI
10.1007/978-3-030-68713-7
Hardcover ISBN
978-3-030-68711-3
Series ISSN
1931-6828
Edition Number
1
Number of Pages
XVI, 541
Number of Illustrations
24 b/w illustrations, 1 illustrations in colour
Topics