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Perturbation Analysis of Optimization Problems. Softcover reprint of the original 1st ed. 2000.
・ISBN 978-1-4612-7129-1 paper EUR 229.99
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| 著者・編者 | Bonnans, J.Frederic / Shapiro, Alexander, |
|---|---|
| シリーズ | Springer Series in Operations Research and Financial Engineering |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2013 |
| ページ数 | 601 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-17810＞ |
解説
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.