Second-Order Duality for Continuous Programming Containing Support Functions

Abstract

A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.

A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.

Keywords

Continuous Programming, Second-Order Invexity, Second-Order Pseudoinvexity, Second-Order Duality, Nonlinear Programming, Support Functions, Natural Boundary Values

Continuous Programming, Second-Order Invexity, Second-Order Pseudoinvexity, Second-Order Duality, Nonlinear Programming, Support Functions, Natural Boundary Values

Cite this paper

nullI. Husain and M. Masoodi, "Second-Order Duality for Continuous Programming Containing Support Functions,"*Applied Mathematics*, Vol. 1 No. 6, 2010, pp. 534-541. doi: 10.4236/am.2010.16071.

nullI. Husain and M. Masoodi, "Second-Order Duality for Continuous Programming Containing Support Functions,"

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