Transversality condition for singular infinite horizon calculus of variations | INSTITUT DE PHYSIQUE DU GLOBE DE PARIS

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  Transversality condition for singular infinite horizon calculus of variations

Publication Type:

Journal Article

Source:

Journal of Global Optimization, Volume 50, Issue 1, p.169-178 (2011)

ISBN:

0925-5001

Accession Number:

WOS:000289293400012

URL:

http://www.springerlink.com/content/r4v737546x602734/

Keywords:

uMR 7154 ; Physico-chimie des Fluides Géologiques ; Keywords Infinite horizon – Calculus of variation – MRAP – Hamilton–Jacobi equation – Transversality condition

Abstract:

We consider an optimal infinite horizon calculus of variations problem linear with respect to the velocities. In this framework the Euler–Lagrange equation are known to be algebraic and thus no informative for the general optimal solutions. We prove that the value of the objective along the MRAPs, the curves that connect as quickly as possible the solutions of the Euler–Lagrange equation, is Lipschitz continuous and satisfies a Hamilton–Jacobi equation in some generalised sense. We derive then a sufficient condition for a MRAP to be optimal by using a transversality condition at infinity that we generalize to our non regular context.

Notes:

Times Cited: 0 SI