Optimal Control of Constrained Self-Adjoint Nonlinear Operator Equations in Hilbert Spaces

M. A. El-Gebeily (), B. S. Mordukhovich () and M. M. Alshahrani ()
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M. A. El-Gebeily: King Fahd University of Petroleum and Minerals
B. S. Mordukhovich: Wayne State University
M. M. Alshahrani: King Fahd University of Petroleum and Minerals

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 3, 735-758

Abstract: Abstract This paper deals with the study of a new class of optimal control problems governed by nonlinear self-adjoint operator equations in Hilbert spaces under general constraints of the equality and inequality types on state variables. While the unconstrained version of such problems has been considered in our preceding publication, the presence of constraints significantly complicates the derivation of necessary optimality conditions. Developing a geometric approach based on multineedle control variations and finite-dimensional subspace extensions of unbounded self-adjoint operators, we establish necessary optimality conditions for the constrained control problems under considerations in an appropriate form of the Pontryagin Maximum Principle.

Keywords: Optimal control; Constrained self-adjoint nonlinear operator equations in Hilbert spaces; Necessary optimality conditions; Maximum principle; 49K20; 47H15; 93C30 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0799-4

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