Optimization Online


A p-Cone Sequential Relaxation Procedure for 0-1 Integer Programs

Samuel Burer (samuel-burer***at***uiowa.edu)
Jieqiu Chen (jieqiu-chen***at***uiowa.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: 02/11/2008
Entry Accepted: 02/11/2008
Entry Last Modified: 06/04/2008

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society