Subdifferential analysis of differential inclusions via discretization

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 inclusi...

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Bibliographic Details
Published in:Journal of Differential Equations Vol. 253; no. 1; pp. 203 - 224
Main Author: Pang, C.H. Jeffrey
Format: Journal Article
Language:English
Published: Elsevier Inc 01.07.2012
Subjects:
Coderivatives
Differential inclusions
Optimality conditions
Reachable map
Subdifferential
Reachable map
Optimality conditions
Differential inclusions
49K40
Subdifferential
49K05
34A60
49K15
Coderivatives
ISSN:0022-0396, 1090-2732
Online Access:Get full text
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.03.019