An elementary sufficiency proof of an absolute minimum for a nonparametric variational problem |
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Authors: | W T Reid |
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Institution: | (1) The University of Oklahoma, Norman, Oklahoma |
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Abstract: | For a fixed endpoint, nonparametric simple integral variational problem, there is presented an expansion method proof of a sufficiency theorem for an absolute minimum. In particular, this sufficiency theorem yields readily the proof of a result of the type recently presented by Nehari (Ref. 1), but with an error in formulation and an incorrect proof. The present discussion is in a setting which permits considered arcs to be on the boundary of the set of admissible arcs; thus it contains as particular instances certain types of unilateral variational problems of a control nature.This research was supported by the National Science Foundation under Grant No. GP-36120. |
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Keywords: | Unilateral variational problems sufficient conditions expansion methods convex analysis Riccati differential inequalities |
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