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＜電子ブック＞
Perturbation Analysis of Optimization Problems / by J.Frederic Bonnans, Alexander Shapiro
(Springer Series in Operations Research and Financial Engineering. ISSN:21971773)

版	1st ed. 2000.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XVIII, 601 p : online resource
著者標目	*Bonnans, J.Frederic author Shapiro, Alexander author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:System theory LCSH:Control theory FREE:Calculus of Variations and Optimization FREE:Systems Theory, Control
一般注記	Basic notation -- Introduction -- Background material -- Optimality conditions -- Basic perturbation theory -- Second order analysis of the optimal value and optimal solutions -- Optimal Control -- References 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 HTTP:URL=https://doi.org/10.1007/978-1-4612-1394-9

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