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

Sun, Xiang-Kai; Li, Sheng-Jie; Zhao, Dan

Taiwanese J. Math. 17, No. 4, 1227-1244 (2013).

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

Keywords:

duality; conjugate function; Farkas-type results; DC infinite programming