On Continuous Programming with Support Functions
- 1 Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India
- 2 Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India
- 3 Department of Statistics, University of Kashmir, Srinagar, India
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.
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