Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems

Parametric and nonparametric necessary and sufficient optimality conditions are established for a class of constrained variational problems containing arbitary norms.Subsequently, the forms and contents of these optimality results are utilized as a basis for constructing two parametric and eight parameter-free duality models and proving appropriate duality theroems. As special cases of these optimality and duality results, similar results are obtained for a related category of variational problems involving square roots of positive semidefinite quadratic forms. The results presented in this paper contain the variational analogues of a fairly large number of cognate results developed previously for various types of smooth and nonsmooth finitedimensional nonlinear programming problems.

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