Subdifferential analysis of differential inclusions via discretization

Details Subdifferential analysis of differential inclusions via discretization Subdifferential analysis of differential inclusions via discretization

2011-12-09

arxiv.org/abs/1112.2116v2

Mathematics

Optimization and Control

20 pages, 1 table. A serious error corrected

Scientific paper

10.1016/j.jde.2012.03.019

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.

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