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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Vydáno v:Journal of Differential Equations Ročník 253; číslo 1; s. 203 - 224
Hlavní autor: Pang, C.H. Jeffrey
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.07.2012
Témata:
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
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Shrnutí: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