Subdifferential analysis of differential inclusions via discretization
Abstract
The framework of differential inclusions encompasses modern optimal control and the calculus of variations. Necessary optimality conditions in the literature identify potentially optimal paths, but do not show how to perturb paths to optimality. We first look at the corresponding discretized inclusions, estimating the subdifferential dependence of the optimal value in terms of the endpoints of the feasible paths. Our approach is to first estimate the coderivative of the reachable map. The discretized (nonsmooth) Euler-Lagrange and transversality conditions follow as a corollary. We obtain corresponding results for differential inclusions by passing discretized inclusions to the limit.
Cite
@article{arxiv.1112.2116,
title = {Subdifferential analysis of differential inclusions via discretization},
author = {C. H. Jeffrey Pang},
journal= {arXiv preprint arXiv:1112.2116},
year = {2012}
}
Comments
I just want to change the comments portion (otherwise article is same as v2). Changes in published version: The assumption that F is osc is added in a few places. The condition (1) in Lemma 5.9 is improved slightly. Added further references, commentary and acknowledgments