Optimality Conditions for Variational Problems in Incomplete Functional Spaces

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 193; no. 1-3; pp. 139 - 157
Main Authors: Mohammadi, Ashkan, Mordukhovich, Boris S.
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Constraints
Continuity (mathematics)
Engineering
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Subspaces
Theory of Computation
Velocity
Variational analysis
Necessary optimality conditions
49J53
49J52
Optimal control
90C48
Calculus of variations
Generalized differentiation
Constrained optimization
49K24
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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 C k as k ≥ 1 .
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01964-2