Overview
- Examines approximate solutions of optimization problems in the presence of computational errors
- Reinforces basic principles with an introductory chapter
- Analyzes the gradient projection algorithm for minimization of convex and smooth functions
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 108)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative.
This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s method.
Reviews
“The author studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space. Researchers and students will find this book instructive and informative. The book has contains 16 chapters … .” (Hans Benker, zbMATH 1347.65112, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Numerical Optimization with Computational Errors
Authors: Alexander J. Zaslavski
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-3-319-30921-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-30920-0Published: 03 May 2016
Softcover ISBN: 978-3-319-80917-5Published: 27 May 2018
eBook ISBN: 978-3-319-30921-7Published: 22 April 2016
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: IX, 304
Topics: Calculus of Variations and Optimal Control; Optimization, Numerical Analysis, Operations Research, Management Science