- A p-Cone Sequential Relaxation Procedure for 0-1 Integer Programs Samuel Burer (samuel-bureruiowa.edu) Jieqiu Chen (jieqiu-chenuiowa.edu) Abstract: 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 ($1 \le p \le \infty$). 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 $p = \infty$, our method corresponds to the well-known procedure of Lov\'asz 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. Keywords: Global optimization, integer programming, second-order cone programming, cone programming, relaxation Category 1: Global Optimization (Theory ) Category 2: Integer Programming (0-1 Programming ) Category 3: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming ) Citation: Manuscript, Department of Management Sciences, University of Iowa, Iowa City, IA 52240, USA, February, 2008 Download: [PDF]Entry Submitted: 02/11/2008Entry Accepted: 02/11/2008Entry Last Modified: 06/04/2008Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.