Abstract
A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions; hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.
Highlights
Chen [1] was the first to identify second-order dual formulated for a constrained variational problem and established various duality results under an involved invexitylike assumptions
A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions; it is nondifferentiable
In the spirit of Mangasarian [5], Husain and Masoodi [6] studied Wolfe type second-order duality for a continuous programming problem having support functions appearing in the integrand of the functional as well as in the constraint functions under second-order invexity and second-order pseudoinvexity conditions
Summary
Chen [1] was the first to identify second-order dual formulated for a constrained variational problem and established various duality results under an involved invexitylike assumptions. In the spirit of Mangasarian [5], Husain and Masoodi [6] studied Wolfe type second-order duality for a continuous programming problem having support functions appearing in the integrand of the functional as well as in the constraint functions under second-order invexity and second-order pseudoinvexity conditions They incorporated a pair of second-order dual variational problems with natural boundary values rather than fixed end points and indicated their close relationship with those of corresponding (static) second-order duality results established for nonlinear programming problem with support functions, considered by Husain et al [7].
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