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.
"DUALITY AND FARKAS-TYPE RESULTS FOR DC INFINITE PROGRAMMING WITH INEQUALITY CONSTRAINTS." Taiwanese J. Math. 17 (4) 1227 - 1244, 2013. https://doi.org/10.11650/tjm.17.2013.2675