Matrix analysis
P-Complete Approximation Problems
Journal of the ACM (JACM)
On Lagrangian Relaxation of Quadratic Matrix Constraints
SIAM Journal on Matrix Analysis and Applications
Approximation of the Stability Number of a Graph via Copositive Programming
SIAM Journal on Optimization
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Solving Lift-and-Project Relaxations of Binary Integer Programs
SIAM Journal on Optimization
Bounds for the quadratic assignment problem using the bundle method
Mathematical Programming: Series A and B
A Copositive Programming Approach to Graph Partitioning
SIAM Journal on Optimization
On the copositive representation of binary and continuous nonconvex quadratic programs
Mathematical Programming: Series A and B
Semidefinite approximations for quadratic programs over orthogonal matrices
Journal of Global Optimization
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
Review: Measuring instance difficulty for combinatorial optimization problems
Computers and Operations Research
Journal of Global Optimization
Computational Optimization and Applications
A note on set-semidefinite relaxations of nonconvex quadratic programs
Journal of Global Optimization
Hi-index | 0.00 |
Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look at tractable approximations and compare with several relaxations from the literature. We show that several of the well-studied models are in fact equivalent. It is still a challenging task to solve the strongest of these models to reasonable accuracy on instances of moderate size.