A p-cone sequential relaxation procedure for 0-1 integer programs

Given a 0-1 integer programming problem, several authors have introduced sequential relaxation techniques — based on linear and/or semidefinite programming — that generate the convex hull of integer points in at most n steps. In this paper, we introduce a sequential relaxation technique, which is based on p-order cone programming (1 ≤ p ≤ ∞). We prove that our technique generates the convex hull of 0-1 solutions asymptotically. In addition, we show that our method generalizes and subsumes several existing methods. For example, when p = ∞, our method corresponds to the wellknown procedure of Lovász and Schrijver based on linear programming (so that finite convergence is obtained by our method in special cases). Although the p-order cone programs in general sacrifice some strength compared to the analogous linear and semidefinite programs, we show that for p = 2 they enjoy a better theoretical iteration complexity. Computational considerations of our technique are also discussed.