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.


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