Journal of Applied Mathematics & Bioinformatics

On Second-Order Fritz John Type Duality for Variational Problems

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• Abstract

  Second-order dual to a variational problem is formulated. This dual uses the Fritz John type necessary optimality conditions instead of the Karush-Kuhn-Tucker type necessary optimality conditions and thus, does not require a constraint qualification. Weak, strong, Mangasarian type strict-converse, and Huard type converse duality theorems between primal and dual problems are established under appropriate generalized second-order invexity conditions. A pair of second-order dual variational problems with natural boundary conditions is constructed, and it is briefly indicated that duality results for this pair can be validated analogously to those for the earlier models dealt with in this research. Finally, it is pointed out that our results can be viewed as the dynamic generalizations of those for nonlinear programming problems, already treated in the literature.