Convexity in Hamilton-Jacobi theory - I: Dynamics and duality

Citation
Rt. Rockafellar et Pr. Wolenski, Convexity in Hamilton-Jacobi theory - I: Dynamics and duality, SIAM J CON, 39(5), 2001, pp. 1323-1350
Citations number
30
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
03630129 → ACNP
Volume
39
Issue
5
Year of publication
2001
Pages
1323 - 1350
Database
ISI
SICI code
0363-0129(20010305)39:5<1323:CIHT-I>2.0.ZU;2-5
Abstract
Value functions propagated from initial or terminal costs and constraints b y way of a differential inclusion, or more broadly through a Lagrangian tha t may take on infinity, are studied in the case where convexity persists in the state argument. Such value functions, themselves taking on infinity, a re shown to satisfy a subgradient form of the Hamilton Jacobi equation whic h strongly supports properties of local Lipschitz continuity, semidifferent iability and Clarke regularity. An extended method of characteristics is de veloped which determines them from the Hamiltonian dynamics underlying the given Lagrangian. Close relations with a dual value function are revealed.