Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

Piermarco Cannarsa, Carlo Sinestrari - Collection Progress in Nonlinear Differential Equations and Their Applications

310 pages, parution le 27/01/2005

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Résumé

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.

Written for: Graduate students and researchers

Sommaire

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
References

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Piermarco Cannarsa, Carlo Sinestrari
Collection	Progress in Nonlinear Differential Equations and Their Applications
Parution	27/01/2005
Nb. de pages	310
Format	15,5 x 23,5
Couverture	Broché
Poids	450g
Intérieur	Noir et Blanc
EAN13	9780817643362
ISBN13	978-0-8176-4336-2