Perturbation Analysis of Optimization Problems

J Frederic Bonnans

ISBN 10: 0387987053 / ISBN 13: 9780387987057

Editore: Springer New York Mai 2000, 2000

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Neuware - 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. Codice articolo 9780387987057

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Titolo: Perturbation Analysis of Optimization ...

Casa editrice: Springer New York Mai 2000

Data di pubblicazione: 2000

Legatura: Buch

Condizione: Neu

Descrizione articolo

Riassunto:

A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.

Contenuti:

Basic notation.- Introduction.- Background material.- Optimality conditions.- Basic perturbation theory.- Second order analysis of the optimal value and optimal solutions.- Optimal Control.- References.