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.
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References
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Communicated by L. Cesari
This research was supported by the National Science Foundation under Grant No. GP-36120.
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Reid, W.T. An elementary sufficiency proof of an absolute minimum for a nonparametric variational problem. J Optim Theory Appl 18, 335–349 (1976). https://doi.org/10.1007/BF00933816
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DOI: https://doi.org/10.1007/BF00933816