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Conjugate Gradient Algorithms in Nonconvex Optimization [electronic resource] /by Radosław Pytlak.

by Pytlak, Radosław [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Nonconvex Optimization and Its Applications: 89Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: XXVI, 477 p. 95 illus. online resource.ISBN: 9783540856344.Subject(s): Mathematics | Mathematical optimization | System safety | Mathematics | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Quality Control, Reliability, Safety and RiskDDC classification: 515.64 Online resources: Click here to access online
Contents:
Conjugate Direction Methods for Quadratic Problems -- Conjugate Gradient Methods for Nonconvex Problems -- Memoryless Quasi-Newton Methods -- Preconditioned Conjugate Gradient Algorithms -- Limited Memory Quasi-Newton Algorithms -- The Method of Shortest Residuals and Nondifferentiable Optimization -- The Method of Shortest Residuals for Differentiable Problems -- The Preconditioned Shortest Residuals Algorithm -- Optimization on a Polyhedron -- Conjugate Gradient Algorithms for Problems with Box Constraints -- Preconditioned Conjugate Gradient Algorithms for Problems with Box Constraints -- Preconditioned Conjugate Gradient Based Reduced-Hessian Methods.
In: Springer eBooksSummary: This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective. Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms. The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented. Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book.
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Item type Current location Call number Status Date due Barcode
QA402.3 (Browse shelf) Available
QA402.5-QA402.6 (Browse shelf) Available
Long Loan MAIN LIBRARY
QA315-316 (Browse shelf) Available

Conjugate Direction Methods for Quadratic Problems -- Conjugate Gradient Methods for Nonconvex Problems -- Memoryless Quasi-Newton Methods -- Preconditioned Conjugate Gradient Algorithms -- Limited Memory Quasi-Newton Algorithms -- The Method of Shortest Residuals and Nondifferentiable Optimization -- The Method of Shortest Residuals for Differentiable Problems -- The Preconditioned Shortest Residuals Algorithm -- Optimization on a Polyhedron -- Conjugate Gradient Algorithms for Problems with Box Constraints -- Preconditioned Conjugate Gradient Algorithms for Problems with Box Constraints -- Preconditioned Conjugate Gradient Based Reduced-Hessian Methods.

This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective. Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms. The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented. Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book.

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