Optimisation et analyse convexe PDF Download

Author: Jean-Baptiste Hiriart-Urruty
Publisher: Presses Universitaires de France - PUF
ISBN:
Category : Convex functions
Languages : fr
Pages : 398

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Author: Jean-Baptiste Hiriart-Urruty
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Michel Willem
Publisher:
ISBN: 9782870852026
Category :
Languages : fr
Pages : 136

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Author: Jean-Pierre Crouzeix
Publisher: Springer Nature
ISBN: 3031306813
Category : Mathematics
Languages : fr
Pages : 204

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De nombreux systèmes physiques, mécaniques, financiers et économiques peuvent être décrits par des modèles mathématiques qui visent à optimiser des fonctions, trouver des équilibres et effectuer des arbitrages. Souvent, la convexité des ensembles et des fonctions ainsi que les conditions de monotonie sur les systèmes d'inéquations qui régissent ces systèmes se présentent naturellement dans les modèles. C'est dans cet esprit que nous avons conçu ce livre en mettant l'accent sur une approche géométrique qui privilégie l'intuition par rapport à une approche plus analytique. Les démonstrations des résultats classiques ont été revues dans cette optique et simplifiées. De nombreux exemples d'applications sont étudiés et des exercices sont proposés. Ce livre s'adresse aux étudiants en master de mathématiques appliquées, ainsi qu'aux doctorants, chercheurs et ingénieurs souhaitant comprendre les fondements de l'analyse convexe et de la théorie des inéquations variationnelles monotones.

Author: Rachid Ellaia
Publisher:
ISBN:
Category :
Languages : fr
Pages : 314

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Author: Michel A. Théra
Publisher: American Mathematical Soc.
ISBN: 9780821821671
Category : Mathematics
Languages : en
Pages : 304

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"This volume presents twenty original refereed papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in nonsmooth and functional analysis with applications to control theory. These papers originated largely from a conference held in conjunction with a 1999 Doctorate Honoris Causa awarded to Jonathan Borwein at Limoges. As such they reflect the areas in which Dr. Borwein has worked. In addition to providing a snapshot of research in the field of modern analysis, the papers suggest some of the directions this research is following at the beginning of the millennium."--BOOK JACKET.

Author: Pierre Alain Mazet
Publisher:
ISBN:
Category :
Languages : fr
Pages : 42

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Author: Dimitri Bertsekas
Publisher: Athena Scientific
ISBN: 1886529450
Category : Mathematics
Languages : en
Pages : 560

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A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. The book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2016), Network Optimization (Athena Scientific, 1998), and Introduction to Linear Optimization (Athena Scientific, 1997). Aside from a thorough account of convex analysis and optimization, the book aims to restructure the theory of the subject, by introducing several novel unifying lines of analysis, including: 1) A unified development of minimax theory and constrained optimization duality as special cases of duality between two simple geometrical problems. 2) A unified development of conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization. 3) A unification of the major constraint qualifications allowing the use of Lagrange multipliers for nonconvex constrained optimization, using the notion of constraint pseudonormality and an enhanced form of the Fritz John necessary optimality conditions. Among its features the book: a) Develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar b) Provides a geometric, highly visual treatment of convex and nonconvex optimization problems, including existence of solutions, optimality conditions, Lagrange multipliers, and duality c) Includes an insightful and comprehensive presentation of minimax theory and zero sum games, and its connection with duality d) Describes dual optimization, the associated computational methods, including the novel incremental subgradient methods, and applications in linear, quadratic, and integer programming e) Contains many examples, illustrations, and exercises with complete solutions (about 200 pages) posted at the publisher's web site http://www.athenasc.com/convexity.html

Author: Jean-Baptiste Hiriart-Urruty
Publisher: Springer Science & Business Media
ISBN: 3642564682
Category : Mathematics
Languages : en
Pages : 268

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This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of bot volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched, making it an excellent choice for the purpose of learning and teaching.

Author: Guy Degla
Publisher: Univ Europeenne
ISBN: 9786131595806
Category :
Languages : fr
Pages : 104

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Cet ouvrage aborde l'Optimisation continue a travers les notions de base de l'Analyse Convexe appliquee et introduit une approche permettant d'obtenir la convergence de solutions optimales d'une suite de fonctions-objectif vers une solution optimale d'un probleme donne; il s'agit de l'epi-convergence encore appelee -convergence due a De Georgi. Cette notion est aussi interessante a cause du fait qu'en dimension finie, l'epi-convergence de fonctions propres semi-continues inferieurement est equivalente a la convergence graphique de leurs epigraphes. L'epi-convergence peut servir a minimiser certaines fonctions objectif ou d'energie echappant a une etude classique a cause d'un defaut de coercivite, de convexite ou de regularite. De plus ses applications s'etendent au Controle Optimal (en Recherche Operationnelle), a la Geometrie des Formes et aux Processus Stochastiques.