A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Self-scaled barriers and interior-point methods for convex programming
Mathematics of Operations Research
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
An Efficient Algorithm for Minimizing a Sum of p-Norms
SIAM Journal on Optimization
Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets
SIAM Journal on Optimization
Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations
Computational Optimization and Applications
Convex Optimization
Subset Algebra Lift Operators for 0-1 Integer Programming
SIAM Journal on Optimization
Solving Lift-and-Project Relaxations of Binary Integer Programs
SIAM Journal on Optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
| Hi-index | 0.00 |
Several authors have introduced sequential relaxation techniques-based on linear and/or semi-definite programming-to generate the convex hull of 0-1 integer points in a polytope 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 well-known procedure of Lovasz and Schrijver based on linear programming. Although the p-order cone programs in general sacrifice some strength compared to the analogous linear and semi-definite programs, we show that for p=2 they enjoy a better theoretical iteration complexity. Computational considerations of our technique are discussed.