Theoretical Mathematics & Applications

Mixed Type Second-order Duality for a Nondifferentiable Continuous Programming Problem

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• Abstract

  A mixed type second-order dual is formulated for a class of continuous programming problem in which the integrand of the objective functional contains square root of positive semi-definite quadratic form; hence it is nondifferentiable. Under second-order pseudoinvexity and second-order quasi-invexity, various duality theorems are proved for this pair of dual nondifferentiable continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and it is briefly indicated that the duality results for this pair of problems can be validated analogously to those for the earlier models. Lastly, it is pointed out that our duality results can be regarded as dynamic generalizations of those for a nondifferentiable nonlinear programming problem, already treated in the literature.