Spectral Functions and Smoothing Techniques on Jordan Algebras: How algebraic techniques can help to design efficient optimization algorithms - Couverture souple

Baes, Michel

 
9783838312101: Spectral Functions and Smoothing Techniques on Jordan Algebras: How algebraic techniques can help to design efficient optimization algorithms
Couverture souple
ISBN 10 : 3838312104 ISBN 13 : 9783838312101
Editeur : LAP Lambert Academic Publishing, 2009

Synopsis

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.

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Présentation de l'éditeur

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.

Biographie de l'auteur

Michel Baes completed his Ph.D. in 2006 at the Center for Operations Research and Econometrics (CORE) in Louvain-la- Neuve under supervision of Pr. Yurii Nesterov. After a Postdoctoral stay at the K.U.Leuven?s Optimization in Engineering Center (OPTEC), he is working now as a senior scientific researcher at ETH in Zurich.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP Lambert Academic Publishing
Date d'édition
2009
Langue
anglais
ISBN 10 
3838312104
ISBN 13 
9783838312101
Reliure
Broché
Nombre de pages
268
Coordonnées du fabricant
non disponible
Personne responsable
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