Michel Baes (5 results)

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Taschenbuch. Condition: Neu. Spectral Functions and Smoothing Techniques on Jordan Algebras | How algebraic techniques can help to design efficient optimization algorithms | Michel Baes | Taschenbuch | 268 S. | Englisch | 2010 | LAP LAMBERT Academic Publishing | EAN 9783838312101 | Verantwortliche Person für die EU: preigu GmbH…& Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu.

Language: English
Published by LAP LAMBERT Academic Publishing Mai 2010 2010
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Convex optimization has witnessed a considerable progress, mainly due to the development of powerful algorithms and software. In fact, one class of convex problems, called self-scaled, can be particularly efficiently solved. This cl…ass encompasses a large amount of real-life convex optimization problems, including linear and semidefinite programming. This class is best described using an algebraic structure known as formally real (or Euclidean) Jordan algebra, which provides an elegant and powerful unifying framework for its study. This book proposes an extensive and self-contained description of these algebras. Our work focuses on the so-called spectral functions on formally real Jordan algebras, a natural generalization of spectral functions of symmetric matrices. Based on an original variational analysis of eigenvalues in Jordan algebras, we discuss their most important properties, such as differentiability and convexity. We show how these results can be applied to extend several algorithms existing for linear or second-order programming to the general class of self-scaled problems, e.g. the powerful smoothing techniques of Nesterov. 268 pp. Englisch.

Language: English
Published by LAP LAMBERT Academic Publishing Mai 2010 2010
- Softcover
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Convex optimization has witnessed a considerable progress, mainly due to the development of powerful algorithms and software. In fact, one class of convex problems, called self-scaled, can be particularly efficiently solved. This class…encompasses a large amount of real-life convex optimization problems, including linear and semidefinite programming. This class is best described using an algebraic structure known as formally real (or Euclidean) Jordan algebra, which provides an elegant and powerful unifying framework for its study. This book proposes an extensive and self-contained description of these algebras. Our work focuses on the so-called spectral functions on formally real Jordan algebras, a natural generalization of spectral functions of symmetric matrices. Based on an original variational analysis of eigenvalues in Jordan algebras, we discuss their most important properties, such as differentiability and convexity. We show how these results can be applied to extend several algorithms existing for linear or second-order programming to the general class of self-scaled problems, e.g. the powerful smoothing techniques of Nesterov.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 268 pp. Englisch.

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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Convex optimization has witnessed a considerable progress, mainly due to the development of powerful algorithms and software. In fact, one class of convex problems, called self-scaled, can be particularly efficiently solved. This class e…ncompasses a large amount of real-life convex optimization problems, including linear and semidefinite programming. This class is best described using an algebraic structure known as formally real (or Euclidean) Jordan algebra, which provides an elegant and powerful unifying framework for its study. This book proposes an extensive and self-contained description of these algebras. Our work focuses on the so-called spectral functions on formally real Jordan algebras, a natural generalization of spectral functions of symmetric matrices. Based on an original variational analysis of eigenvalues in Jordan algebras, we discuss their most important properties, such as differentiability and convexity. We show how these results can be applied to extend several algorithms existing for linear or second-order programming to the general class of self-scaled problems, e.g. the powerful smoothing techniques of Nesterov.