Optimality Conditions for Variational Problems in Incomplete Functional Spaces

Ashkan Mohammadi () and Boris S. Mordukhovich ()
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Ashkan Mohammadi: Georgetown University
Boris S. Mordukhovich: Wayne State University

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 9, 139-157

Abstract: Abstract This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach consists of reducing a variational problem to a (nondynamic) problem of constrained optimization in a normed space and then applying the results recently obtained for the latter class by using generalized differentiation. In this way, we derive necessary optimality conditions for nonconvex problems of the calculus of variations with velocity constraints under the weakest metric subregularity-type constraint qualification. The developed approach leads us to a short and simple proof of first-order necessary optimality conditions for such and related problems in broad spaces of functions including those of class $${{\mathcal {C}}}^k$$ C k as $$k\ge 1$$ k ≥ 1 .

Keywords: Calculus of variations; Constrained optimization; Optimal control; Necessary optimality conditions; Variational analysis; Generalized differentiation; 49K24; 49J52; 49J53; 90C48 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01964-2

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