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Second-Order Duality for Continuous Programming Containing Support Functions
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Applied Mathematics·Volume 01 (2010)·Pages 534–541·Published 27 December 2010·DOI10.4236/am.2010.16071
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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.
KeywordsContinuous ProgrammingSecond-Order InvexitySecond-Order PseudoinvexitySecond-Order DualityNonlinear ProgrammingSupport FunctionsNatural Boundary Values
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