1. Optimality Conditions for Variational Problems in Incomplete Functional Spaces
- Author
-
Boris S. Mordukhovich and Ashkan Mohammadi
- Subjects
Class (set theory) ,021103 operations research ,Control and Optimization ,Applied Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,Constrained optimization ,02 engineering and technology ,Management Science and Operations Research ,Absolute continuity ,01 natural sciences ,Linear subspace ,Constraint (information theory) ,Simple (abstract algebra) ,Metric (mathematics) ,Applied mathematics ,0101 mathematics ,Normed vector space ,Mathematics - 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 involves 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 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 the First-order necessary optimality conditions for such and related problems in broad spaces of functions, including those of class C^k.
- Published
- 2021