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On Continuous Programming with Support Functions

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DOI: 10.4236/am.2013.410194    2,858 Downloads   4,126 Views   Citations


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.

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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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