When does strong duality fail in linear programming? When does strong duality fail in linear programming? I have considered the case when both primal and dual solutions are infeasible, but then there are no optimal solutions at all.
The strong duality theorem of linear programming states that (quoted from "Algorithms" by S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani, 2006) "If a linear program has a bounded optimum, then so does its dual, and the two optimum values coincide." Hence, it never fails.