Necessary and Sufficient Conditions for Optimality of Nonconvex, Noncoercive Autonomous Variational Problems with Constraints
Abstract
We consider one-dimensional autonomous constrained variational
problems with possibly nonsmooth, nonconvex, noncoercive integrands.
We prove a necessary and sufficient condition for the optimality
of a trajectory in the form of a DuBois-Reymond inclusion involving the subdifferential
of Convex Analysis.
Moreover, we also provide a relaxation result and necessary and
sufficient conditions for the existence of the minimum expressed
in terms of the boundary data. Applications to various noncoercive
variational problems are also included.
[DOI: 10.1685 / CSC06109] About DOI
problems with possibly nonsmooth, nonconvex, noncoercive integrands.
We prove a necessary and sufficient condition for the optimality
of a trajectory in the form of a DuBois-Reymond inclusion involving the subdifferential
of Convex Analysis.
Moreover, we also provide a relaxation result and necessary and
sufficient conditions for the existence of the minimum expressed
in terms of the boundary data. Applications to various noncoercive
variational problems are also included.
[DOI: 10.1685 / CSC06109] About DOI
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PDFDOI: https://doi.org/10.1685/
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