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Cover: 9781461271291 | Perturbation Analysis of Optimization Problems | Shapiro (u. a.)
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Perturbation Analysis of Optimization Problems
Taschenbuch von Alexander Shapiro (u. a.)
Sprache: Englisch

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Beschreibung
The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.
The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.
Zusammenfassung
This is a research-level book in optimization. The results herein can be applied to various fields, from physics to economics. A nice feature is its great number of examples, which help the reader to understand the meaning of various statements and assumptions. It will be very useful not only to research professionals in the field of optimization, nonlinear programming and optimal control, but also to users of optimization in mechanics, physics, statistics, finance and economics.
Inhaltsverzeichnis
Basic notation.- Introduction.- Background material.- Optimality conditions.- Basic perturbation theory.- Second order analysis of the optimal value and optimal solutions.- Optimal Control.- References.
Details
Erscheinungsjahr: 2013
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
601 S.
ISBN-13: 9781461271291
ISBN-10: 1461271290
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Shapiro, Alexander
Bonnans, J. Frederic
Auflage: Softcover reprint of the original 1st edition 2000
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 34 mm
Von/Mit: Alexander Shapiro (u. a.)
Erscheinungsdatum: 15.11.2013
Gewicht: 0,931 kg
Artikel-ID: 105322843
Zusammenfassung
This is a research-level book in optimization. The results herein can be applied to various fields, from physics to economics. A nice feature is its great number of examples, which help the reader to understand the meaning of various statements and assumptions. It will be very useful not only to research professionals in the field of optimization, nonlinear programming and optimal control, but also to users of optimization in mechanics, physics, statistics, finance and economics.
Inhaltsverzeichnis
Basic notation.- Introduction.- Background material.- Optimality conditions.- Basic perturbation theory.- Second order analysis of the optimal value and optimal solutions.- Optimal Control.- References.
Details
Erscheinungsjahr: 2013
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
601 S.
ISBN-13: 9781461271291
ISBN-10: 1461271290
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Shapiro, Alexander
Bonnans, J. Frederic
Auflage: Softcover reprint of the original 1st edition 2000
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 34 mm
Von/Mit: Alexander Shapiro (u. a.)
Erscheinungsdatum: 15.11.2013
Gewicht: 0,931 kg
Artikel-ID: 105322843
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