Volume 10, Number 1, January 2004
|Page(s)||123 - 141|
|Published online||15 February 2004|
Turnpike theorems by a value function approach
UMR Analyse des Systèmes et Biométrie,
2, place Viala, 34060 Montpellier, France;
2 GREQAM, université de la Méditerranée, 2, rue de la Vieille Charité, 13002 Marseille, France; email@example.com.
Revised: 6 August 2003
Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness of the singular solution. We provide a new necessary and sufficient condition for turnpike optimality, even in the presence of multiple singular solutions.
Mathematics Subject Classification: 34H05 / 49K05 / 49L25
Key words: Calculus of variations / infinite horizon / Hamilton-Jacobi equation / viscosity solutions / turnpike.
© EDP Sciences, SMAI, 2004
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.