Optimization algorithms on matrix manifolds / P.-A. Absil, R. Mahony, R. Sepulchre.

By: Absil, P.-A [author.]
Contributor(s): Mahony, R. (Robert), 1967- [author.] | Sepulchre, R. (Rodolphe), 1967- [author.]
Material type: TextTextPublisher: Princeton, N.J. ; Woodstock : Princeton University Press, ©2008Description: 1 online resource (xiv, 224 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9781400830244; 1400830249Subject(s): Mathematical optimization | Matrices | Algorithms | Optimisation mathématique | Matrices | Algorithmes | MATHEMATICS -- Numerical Analysis | MATHEMATICS -- Applied | Algorithms | Mathematical optimization | Matrices | Matriser (matematik) | Optimering | AlgoritmerGenre/Form: Electronic book. | Electronic books. Additional physical formats: Print version:: Optimization algorithms on matrix manifolds.DDC classification: 518.1 LOC classification: QA402.5 | .A27 2008ebOther classification: SK 915 Online resources: Click here to access online
Contents:
Introduction -- Motivation and applications -- Matrix manifolds : first-order geometry -- Line-search algorithms on manifolds -- Matrix manifolds : second-order geometry -- Newton's method -- Trust-region methods -- A constellation of superlinear algorithms.
Summary: Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differentia.
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Includes bibliographical references and index.

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differentia.

Print version record.

Introduction -- Motivation and applications -- Matrix manifolds : first-order geometry -- Line-search algorithms on manifolds -- Matrix manifolds : second-order geometry -- Newton's method -- Trust-region methods -- A constellation of superlinear algorithms.

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Optimization algorithms on matrix manifolds / by Absil, P.-A. ©2008

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