This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control.

Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students in optimization, control theory, and pure and applied mathematics.

Reviews

"The style of exposition is lively, engaging, incisive sometimes; a real and successful effort has been made to render the material accessible to nonspecialists of the subject."

-- Zentralblatt MATH

Table of Contents

• Motivation
• Existence of solutions (chapter 2)
• Variational principles
• The geometry of nonsmooth analysis (chapter 4)
• Subgradient calculus
• Necessary conditions in dynamic optimization
• Dynamic programming