Zero duality gap in integer programming: P-norm surrogate constraint method

A p-norm surrogate constraint method is proposed in this paper for integer programming. A single surrogate constraint can be always constructed using p-norm such that the feasible sets in a surrogate relaxation and the primal problem match exactly. The p-norm surro-gate constraint method is thus guaranteed to succeed in identifying the optimal solution of the primal problem with zero duality gap. The existence of a saddle point is proven for integer programming problems. The theory of integer programming has been advanced in this paper by answering the fundamental questions of duality gap elimination and existence of saddle point.