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Duality and Farkas-type results for DC infinite programming with inequality constraints. (English) Zbl 1276.49028

Summary: In this paper, a DC infinite programming problem with inequality constraints is considered. By using the method of Fenchel conjugate functions, a dual scheme for the DC infinite programming problem is introduced. Then, under suitable conditions, weak and strong duality assertions are obtained. Moreover, by using the obtained duality assertions, some Farkas-type results which characterize the optimal value of the DC infinite programming problem are given. As applications, the proposed approach is applied to conic programming problems.

MSC:

49N15 Duality theory (optimization)
90C32 Fractional programming
90C46 Optimality conditions and duality in mathematical programming
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