A computational study of graph partitioning
Mathematical Programming: Series A and B
Recent directions in netlist partitioning: a survey
Integration, the VLSI Journal
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
Semidefinite programming relaxations for the graph partitioning problem
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
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
SIAM Journal on Optimization
On the copositive representation of binary and continuous nonconvex quadratic programs
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Lower bounds for the partitioning of graphs
IBM Journal of Research and Development
Copositive and semidefinite relaxations of the quadratic assignment problem
Discrete Optimization
On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming
Mathematics of Operations Research
| Hi-index | 0.00 |
Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from $${\mathbb{R}^{n\times k}}$$ , then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower bounds for several problems from combinatorial optimization, like the Graph partitioning problem (GPP), the Quadratic assignment problem (QAP) etc. In particular we show how to improve significantly the well-known Donath-Hoffman eigenvalue lower bound for GPP by semidefinite programming. In the last part of the paper we show that the copositive strengthening of the semidefinite lower bounds for GPP and QAP yields the exact values.