Perturbation analysis of optimization problems

✍ Scribed by J. Frédéric Bonnans, Alexander Shapiro (auth.)

• Publisher: Springer-Verlag New York
• Year: 2000
• Tongue: English
• Leaves: 618
• Series: Springer series in operations research
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xviii
Introduction....Pages 1-7
Background Material....Pages 8-145
Optimality Conditions....Pages 146-259
Stability and Sensitivity Analysis....Pages 260-400
Additional Material and Applications....Pages 401-526
Optimal Control....Pages 527-569
Bibliographical Notes....Pages 570-582
Back Matter....Pages 583-601

✦ Subjects

Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control