Nonlinear Phenomena in Complex Systems, 2004, Vol.7, No.1, pp.85-91

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2004, Vol.7, No.1, pp.85-91

Local Selectors and Refined Necessary Optimality Conditions for Differential Inclusions with Delay
L.I.Minchenko and A.A.Volosevich

Method of local selectors has been introduced by V. G. Bolt'yanski for deriving necessary optimality conditions of maximum principle type in the optimal control problem for differential inclusions. The interesting feature of Bolt'yanski's maximum principle is that it depends on the choice of local selector and, therefore, there exists a family of necessary conditions by Bolt'yanski. In the paper the optimal control problem for the differential inclusions with delay is considered. The goal of the paper is to derive refined necessary conditions which don't need using local selectors but include all possible Bolt'yanski's maximum principles.
Key words: Differential inclusions, optimization, nonsmooth analysis, set-valued functions

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