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Optimal Control of Semilinear Unbounded Evolution Inclusions with Functional Constraints

Author

Listed:
  • Boris S. Mordukhovich

    (Wayne State University)

  • Dong Wang

    (Fayetteville State University)

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.

Suggested Citation

  • Boris S. Mordukhovich & Dong Wang, 2015. "Optimal Control of Semilinear Unbounded Evolution Inclusions with Functional Constraints," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 821-841, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0301-0
    DOI: 10.1007/s10957-013-0301-0
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