IJPAM: Volume 77, No. 5 (2012)

FILIPPOV APPROACH IN NECESSARY CONDITIONS OF
OPTIMALITY FOR SINGULAR CONTROL PROBLEM

Mokhtar Hafayed$^1$, Syed Abbas$^2$
Laboratory of Applied Mathematics
Mohamed Khider University
P.O. Box 145, Biskra, 07000, ALGERIA
School of Basic Sciences
Indian Institute of Technology Mandi
Mandi, 175001, INDIA


Abstract. This paper deals with optimal singular stochastic control problem for systems governed by nonlinear stochastic differential equations (SDEs for short) with Lipschitz coefficients, where the control variable has two components, the first being absolutely continuous and the second singular. We apply Ekeland's variational principle to establish necessary conditions for near-optimality. Filippov approach and stable convergence of probability measure are applied to prove our maximum principle.

Received: October 26, 2011

AMS Subject Classification: 93E20, 60H10, 34F05

Key Words and Phrases: singular stochastic control, Filippov approach, nonsmooth maximum principle, stable convergence, Ekeland's variational principle

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 5