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Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control : Progress in Nonlinear Differential Equations and Their Applications - Piermarco Cannarsa

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

Progress in Nonlinear Differential Equations and Their Applications


Published: 14th September 2004
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Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations.

The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.

"The main purpose of this book is to provide a systematic study of the notion of semiconcave functions, as well as a presentation of mathematical fields in which this notion plays a fundamental role. Many results are extracted from articles by the authors and their collaborators, with simplified-and often new-presentation and proofs.... One of the most attractive features of this book is the interplay between several fields of mathematical analysis.... Despite the many topics addressed in the book, the required mathematical background for reading it is limited because all the necessary notions are not only recalled, but also carefully explained, and the main results proved.

The book will be found very useful by experts in nonsmooth analysis, nonlinear control theory and PDEs, in particular, as well as by advanced graduate students in this field. They will appreciate the many detailed examples, the clear proofs and the elegant style of presentation, the fairly comprehensive and up-to-date bibliography and the very pertinent historical and bibliographical comments at the end of each chapter."

-Mathematical Reviews

A Model Problem
Semiconcave Functions
Generalized Gradients and Semiconcavity
Singularities of Semiconcave Functions
Hamilton-Jacobi Equations
Calculus of Variations
Optimal Control Problems
Control Problems with Exit Time
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780817643362
ISBN-10: 0817643362
Series: Progress in Nonlinear Differential Equations and Their Applications
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 304
Published: 14th September 2004
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.6
Weight (kg): 1.0