Convex Quadratic Programming for Exact Solution of 0-1 Quadratic Programs

Let (QP ) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear constraints. In this paper, we present a general method to solve (QP ) by reformulation of the problem into an equivalent 0-1 program with a convex quadratic objective function, followed by the use of a standard mixed integer quadratic programming solver. Our convexification method, which is the best in a certain sense, uses the equality constraints of (QP ) and requires the solution of a semidefinite program. We apply it to the densest k-subgraph problem and report experimental results showing that, for this graph problem, the approach outperforms existing methods. Keyword : Quadratic 0-1 programming, Convex quadratic programming, semidefinite programming, densest k-subgraph, Experiments.