A novel method is disclosed for efficiently solving minimax problems, and in particular, for efficiently solving minimax problems wherein the corresponding matrix is large. In particular, the novel method solves minimax problems in O(n2 T) operation count, where n denotes the problem size and T is reversely proportional to the required duality gap as one skilled in the art will understand. Further disclosed herein is a method for solving linear programming (LP) problems by converting such problems into minimax problems, and then using the novel minimax solution method disclosed herein.