Optimal Control of Semilinear Unbounded Evolution Inclusions with Functional Constraints

Boris S. Mordukhovich () and Dong Wang ()
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Boris S. Mordukhovich: Wayne State University
Dong Wang: Fayetteville State University

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 4, 841 pages

Abstract: Abstract This paper is devoted to the study of a Mayer-type optimal control problem for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces subject to endpoint constraints described by finitely many Lipschitzian equalities and inequalities. First we construct a sequence of discrete approximations to the optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of variational analysis and generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for continuous-time evolution inclusions by passing to the limit from discrete approximations.

Keywords: Optimal control; Variational analysis; Generalized differentiation; Semilinear evolution inclusions; Discrete approximations; Necessary optimality conditions (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-013-0301-0

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