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The relaxed stochastic maximum principle in singular optimal control of diffusions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
2007 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 46, no 2, 427-444 p.Article in journal (Refereed) Published
Abstract [en]

This paper studies optimal control of systems driven by stochastic differential equations, where the control variable has two components, the first being absolutely continuous and the second singular. Our main result is a stochastic maximum principle for relaxed controls, where the first part of the control is a measure valued process. To achieve this result, we establish first order optimality necessary conditions for strict controls by using strong perturbation on the absolutely continuous component of the control and a convex perturbation on the singular one. The proof of the main result is based on the strict maximum principle, Ekeland's variational principle, and some stability properties of the trajectories and adjoint processes with respect to the control variable.

Place, publisher, year, edition, pages
2007. Vol. 46, no 2, 427-444 p.
Keyword [en]
singular control, maximum principle, adjoint process, variational, inequality, relaxed control, variational principle
Identifiers
URN: urn:nbn:se:kth:diva-16674DOI: 10.1137/050644744ISI: 000246923600003Scopus ID: 2-s2.0-41449088749OAI: oai:DiVA.org:kth-16674DiVA: diva2:334717
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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Djehiche, Boualem

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