The contingent epiderivative and the calculus of variations on time scales

Details The contingent epiderivative and the calculus of variations on time scales The contingent epiderivative and the calculus of variations on time scales

2010-07-03

arxiv.org/abs/1007.0509v1

Optimization 61 (2012), no. 3, 251--264

Mathematics

Optimization and Control

Submitted 06/March/2010; revised 12/May/2010; accepted 03/July/2010; for publication in "Optimization---A Journal of Mathemati

Scientific paper

10.1080/02331934.2010.506615

The calculus of variations on time scales is considered. We propose a new approach to the subject that consists in applying a differentiation tool called the contingent epiderivative. It is shown that the contingent epiderivative applied to the calculus of variations on time scales is very useful: it allows to unify the delta and nabla approaches previously considered in the literature. Generalized versions of the Euler-Lagrange necessary optimality conditions are obtained, both for the basic problem of the calculus of variations and isoperimetric problems. As particular cases one gets the recent delta and nabla results.

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