Synopses & Reviews
This monograph provides a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important application in science and technology, has experienced an impressive development during the last two decades. This monograph aims to address some of the pressing unsolved questions in the field. The exposition concentrates along two main directions: the optimal control of linear and nonlinear elliptic equations, and problems involving unknown and/or variable domains. Throughout this monograph, the authors elucidate connections between seemingly different types of problems. One basic feature is to relax the needed regularity assumptions as much as possible in order to include larger classes of possible applications. The book is organized into six chapters that give a gradual and accessible presentation of the material, and a special effort is made to present numerous examples. This monograph is addressed primarily to mathematics graduate students and researchers, however much of this material will also prove useful for scientists from physics, mechanics, and engineering.
From the reviews of the first edition:
This book gives a comprehensive view of the optimization of systems governed by partial differential equations of elliptic type. ? The book is carefully written. ? The book will therefore be useful for experienced researchers as well as students willing to enter the field. One could even teach a graduate course by selecting material from the book." (J. Fr?d?ric Bonnans, Mathematical Reviews, Issue 2006 j)"
From the reviews: "The book gives a comprehensive view of the optimization of systems governed by partial differential equations of elliptic type. ... The book is carefully written. Basic tools of convex analysis, an abstract optimization theory, notions on the well-posedness of elliptic systems, and the existence results for optimal control problems are presented in a simple way. ... The book will therefore be useful for confirmed researchers as well as students willing to enter in the field. One could even teach a graduate course by selecting material." (Joseph Frédéric Bonnans, Zentralblatt MATH, Vol. 1106 (8), 2007)
Table of Contents
Preface.- Introductory topics.- Existance.- Optimality conditions.- Discretization.- Unknown domains.- Optimization of curved mechanical systems.- Appendix 1: Convex mappings and monotone operators.- Appendix 2: Elliptic equations and variational inequalities.- Appendix 3: Domain convergence.- References.