Shapes and Geometries: Analysis, Differential Calculus, and Optimization

This book provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. Shapes and Geometries: Analysis, Differential Calculus, and Optimization presents the extensive, recently developed theoretical foundation to shape optimization in a form that can be used by the engineering community. It also clearly explains the state-of-the-art developments in a mathematical language that will attract mathematicians to open questions in this important field.

M. C. Delfour is a Professor of Mathematics and Statistics at the University of Montreal in Canada and a member of the Canadian Academy of Sciences (FRSC). His areas of research are the analysis and control of delay and distributed parameter systems, the control and stabilization of large flexible space structures, and numerical methods in differential equations and optimization. His recent interests include shape optimal design, modeling of thin and asymptotic shells, and problems in frequency spectrum assignments to land mobiles systems. He is the author or coauthor of several books and more than 100 papers. He has served on numerous Canadian advisory boards and granting committees and on international panels and committees. He was president of the Canadian Mathematical Society from 1992 to 1994. He has been Professional Engineer since 1966 and is still actively involved in consulting for Canadian organizations.

J.-P. Zolésio is Research Director at the CNRS at INRIA, Sophia-Antipolis, France. His areas of research are shape optimization, control of large flexible structures, free boundary problems in Plasma Physics, and control of non-cylindrical problems. In 1998 he was assigned to the Centre de Mathématiques Appliquées of the École des Mines where he participated in the development of an industrial applications program. He organized several international conferences on shape analysis for the IFIP and COMCON federations and received the IFIP Silver Core in 1992. He is the author or coauthor of several books and more than 100 papers, and he has directed more than 20 doctoral theses on the theory and applications of shape analysis.