On Continuous Programming with Support Functions

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Husain, I. , Shrivastav, S. and Shah, A. (2013) On Continuous Programming with Support Functions. Applied Mathematics, 4, 1441-1449. doi: 10.4236/am.2013.410194.

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