J.Frederic Bonnans – författare

This book presents general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems. These results may be applied to various fields, from physics to economics, as various examples in the book show. Therefore, the book is an opportunity for popularizing these techniques among researchers involved in other sciences. Consequently the readership should be not only researchers in the field of optimization, nonlinear programming and optimal control, but also users of optimization in a wide sense, in mechanics (elasticity and plasticity theory), physics, statistics, finance and economics. The book will be useful to research professionals, including graduate students at an advanced level.

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.