Duality in Semi-Infinite Linear Programming

For the case of a consistent semi-infinite linear program, we provide several hypotheses, which are both necessary as well as sufficient, that there be no duality gap between the program and its formal dual (with attainment of value in the dual), for every linear objective function. Earlier work provided sufficient conditions for no duality gap for all linear objective functions, or a necessary and sufficient condition for no duality gap for a fixed linear criterion.