Zdenek Dostál

Optimal Quadratic Programming Algorithms

With Applications to Variational Inequalities

• Broschiertes Buch

Produktbeschreibung

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 theseimprovements 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.

Produktdetails

• Springer Optimization and its Applications 23
• Verlag: Springer / Springer US / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-4648-5
• Softcover reprint of hardcover 1st ed. 2009
• Seitenzahl: 304
• Erscheinungstermin: 8. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 17mm
• Gewicht: 457g
• ISBN-13: 9781441946485
• ISBN-10: 1441946489
• Artikelnr.: 32864755

Inhaltsangabe

Preface.- Part I Background.- 1. Linear Algebra.- 2. Optimization.- Part II Algorithms.- 3. Conjugate Gradients for Unconstrained Minimization.- 4. Equality Constrained Minimization.- 5. Bound Constrained Minimization.- 6. Bound and Equality Constrained Minimization.- Part III Applications to Variational Inequalities.- 7. Solution of a Coercive Variational Inequality by FETI-DP method.- 8. Solution to a Semicoercive Variational Inequality by TFETI Method.- References.- Index.

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I Background.- Linear Algebra.- Optimization.- II Algorithms.- Conjugate Gradients for Unconstrained Minimization.- Equality Constrained Minimization.- Bound Constrained Minimization.- Bound and Equality Constrained Minimization.- III Applications to Variational Inequalities.- Solution of a Coercive Variational Inequality by FETI#x2014;DP Method.- Solution of a Semicoercive Variational Inequality by TFETI Method.