Overview
- The first monograph to present the solution to quadratic programming problems, a topic usually addressed only in journal publications
- Offers theoretical and practical results in the field of bound-constrained and equality-constrained optimization
- Provides algorithms with the rate of convergence independent of constraints
- Develops theoretically supported scalable algorithms for variational inequalities
- Comprehensive presentation of working set methods and inexact augmented Lagrangians
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 23)
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Table of contents (8 chapters)
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Front Matter
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Background
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Front Matter
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Part I Background
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Algorithms
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Front Matter
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Applications to Variational Inequalities
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Front Matter
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Part III Applications to Variational Inequalities
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Back Matter
Keywords
About this book
Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is a valuable resource in nearly every scientific field.
Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments.
This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming. The reader is required to have a basic knowledge of calculus in several variables and linear algebra.
Bibliographic Information
Book Title: Optimal Quadratic Programming Algorithms
Book Subtitle: With Applications to Variational Inequalities
Authors: Zdenek Dostál
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/b138610
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2009
Hardcover ISBN: 978-0-387-84805-1Published: 05 March 2009
Softcover ISBN: 978-1-4419-4648-5Published: 08 December 2010
eBook ISBN: 978-0-387-84806-8Published: 03 April 2009
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: XVII, 284
Number of Illustrations: 2 b/w illustrations
Topics: Calculus of Variations and Optimal Control; Optimization, Operations Research, Management Science, Mathematical and Computational Engineering, Numerical Analysis