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This book includes variants of the ellipsoid method for convex and quasiconvex problems and applies them to very general convex and quasiconvex models in location theory. It starts by des… Plus…

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dos Santos Gromicho, J.A.:
Quasiconvex Optimization and Location Theory (Applied Optimization, 9) - edition reliée, livre de poche

1998

ISBN: 9780792346944

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Quasiconvex Optimization and Location Theory (Applied Optimization, 9) - edition reliée, livre de poche

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Quasiconvex Optimization and Location Theory - edition reliée, livre de poche

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Quasiconvex Optimization and Location Theory (Applied Optimization, 9)

This book includes variants of the ellipsoid method for convex and quasiconvex problems and applies them to very general convex and quasiconvex models in location theory. It starts by describing the adopted notation and provides basic details of convexity and convex optimization. Without aiming at replacing classical references, it manages to bring the required concepts into an easily tractable form and to focus the reader on the more elaborate developments that follow. Many techniques in convex optimization rely on the use of separation hyperplanes. The book uses the ellipsoid method as an illustration of such a technique and provides a new and more stable version of this method. The new algorithm receives a clear and concise treatment, starting with its derivation and ending with its convergence analysis. Both the derivation and the analysis use a simpler approach than previously found in the literature. The second part of the book generalizes the new algorithm to solve quasiconvex programs. Although the techniques required by the quasiconvex case are more complex, the book provides a clear and direct interpretation of the main theoretical results. Audience: This book will be of great value to graduate students and researchers working in continuous optimization using separation techniques and for those dealing with general continuous location models.

Informations détaillées sur le livre - Quasiconvex Optimization and Location Theory (Applied Optimization, 9)


EAN (ISBN-13): 9780792346944
ISBN (ISBN-10): 0792346947
Version reliée
Date de parution: 1998
Editeur: Springer
240 Pages
Poids: 0,522 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-04-13T12:00:22+02:00 (Paris)
Page de détail modifiée en dernier sur 2023-12-29T13:16:20+01:00 (Paris)
ISBN/EAN: 0792346947

ISBN - Autres types d'écriture:
0-7923-4694-7, 978-0-7923-4694-4
Autres types d'écriture et termes associés:
Auteur du livre: dos santos, san antonio
Titre du livre: location theory, theory wants


Données de l'éditeur

Auteur: J.A. dos Santos Gromicho
Titre: Applied Optimization; Quasiconvex Optimization and Location Theory
Editeur: Springer; Springer US
219 Pages
Date de parution: 1998-01-31
New York; NY; US
Langue: Anglais
106,99 € (DE)
109,99 € (AT)
118,00 CHF (CH)
Available
XXII, 219 p.

BB; Hardcover, Softcover / Mathematik/Sonstiges; Optimierung; Verstehen; algorithms; classification; complexity; computation; derivative; derivatives; dynamic programming; Facility Location; geometry; optimization; programming; sets; Subdifferential; Optimization; Algorithms; Computational Mathematics and Numerical Analysis; Theory of Computation; Econometrics; Algorithmen und Datenstrukturen; Numerische Mathematik; Theoretische Informatik; Ökonometrie und Wirtschaftsstatistik; EA; BC

1 Introduction.- 2 Elements of Convexity.- 2.1 Generalities.- 2.2 Convex sets.- 2.3 Convex functions.- 2.4 Quasiconvex functions.- 2.5 Other directional derivatives.- 3 Convex Programming.- 3.1 Introduction.- 3.2 The ellipsoid method.- 3.3 Stopping criteria.- 3.4 Computational experience.- 4 Convexity in Location.- 4.1 Introduction.- 4.2 Measuring convex distances.- 4.3 A general model.- 4.4 A convex location model.- 4.5 Characterizing optimality.- 4.6 Checking optimality in the planar case.- 4.7 Computational results.- 5 Quasiconvex Programming.- 5.1 Introduction.- 5.2 A separation oracle for quasiconvex functions.- 5.3 Easy cases.- 5.4 When we meet a “bad” point.- 5.5 Convergence proof.- 5.6 An ellipsoid algorithm for quasiconvex programming.- 5.7 Improving the stopping criteria.- 6 Quasiconvexity in Location.- 6.1 Introduction.- 6.2 A quasiconvex location model.- 6.3 Computational results.- 7 Conclusions.

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