Stationarity and Convergence in Reduce-or-Retreat Minimization - Couverture souple

Livre 5 sur 43: SpringerBriefs in Optimization

Levy, Adam B.

 
9781461446415: Stationarity and Convergence in Reduce-or-Retreat Minimization
Couverture souple
ISBN 10 : 1461446414 ISBN 13 : 9781461446415
Editeur : Springer, 2012

Synopsis

Stationarity and Convergence in Reduce-or-Retreat Minimization presents and analyzes a unifying framework for a wide variety of numerical methods in optimization. The author's 'reduce-or-retreat' framework is a conceptual method-outline that covers any method whose iterations choose between reducing the objective in some way at a trial point, or retreating to a closer set of trial points. The alignment of various derivative-based methods within the same framework encourages the construction of new methods, and inspires new theoretical developments as companions to results from across traditional divides. The text illustrates the former by developing two generalizations of classic derivative-based methods which accommodate non-smooth objectives, and the latter by analyzing these two methods in detail along with a pattern-search method and the famous Nelder-Mead method. In addition to providing a bridge for theory through the 'reduce-or-retreat' framework, this monograph extends and broadens the traditional convergence analyses in several ways. Levy develops a generalized notion of approaching stationarity which applies to non-smooth objectives, and explores the roles of the descent and non-degeneracy conditions in establishing this property. The traditional analysis is broadened by considering 'situational' convergence of different elements computed at each iteration of a reduce-or-retreat method. The 'reduce-or-retreat' framework described in this text covers specialized minimization methods, some general methods for minimization and a direct search method, while providing convergence analysis which complements and expands existing results.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Stationarity and Convergence in Reduce-or-Retreat Minimization presents and analyzes a unifying framework for a wide variety of numerical methods in optimization. The author's 'reduce-or-retreat' framework is a conceptual method-outline that covers any method whose iterations choose between reducing the objective in some way at a trial point, or retreating to a closer set of trial points. The alignment of various derivative-based methods within the same framework encourages the construction of new methods, and inspires new theoretical developments as companions to results from across traditional divides. The text illustrates the former by developing two generalizations of classic derivative-based methods which accommodate non-smooth objectives, and the latter by analyzing these two methods in detail along with a pattern-search method and the famous Nelder-Mead method. In addition to providing a bridge for theory through the 'reduce-or-retreat' framework, this monograph extends and broadens the traditional convergence analyses in several ways. Levy develops a generalized notion of approaching stationarity which applies to non-smooth objectives, and explores the roles of the descent and non-degeneracy conditions in establishing this property. The traditional analysis is broadened by considering 'situational' convergence of different elements computed at each iteration of a reduce-or-retreat method. The 'reduce-or-retreat' framework described in this text covers specialized minimization methods, some general methods for minimization and a direct search method, while providing convergence analysis which complements and expands existing results.

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

Éditeur
Springer
Date d'édition
2012
Langue
anglais
ISBN 10 
1461446414
ISBN 13 
9781461446415
Reliure
Broché
Nombre de pages
68
Coordonnées du fabricant
non disponible
Personne responsable
CMN Printpool Inh. Mathis Neumann
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Hamburg
Allemagne

Autres éditions populaires du même titre

9781461446422: Stationarity and Convergence in Reduce-Or-Retreat Minimization

Edition présentée

ISBN 10 :  1461446422 ISBN 13 :  9781461446422
Editeur : Not Avail, 2014
Couverture souple