Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation

Improving standard solvers convex reformulation for constrained quadratic 0-1 programs: the QCR method

Let (QP ) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear equality constraints. In this paper, we present QCR, a general method to reformulate (QP ) into an equivalent 0-1 program with a convex quadratic objective function. The reformulated problem can then be efficiently solved by a classical branch-and-bound algorithm, based on continuous relaxat...

Quadratic 0-1 programming: Tightening linear or quadratic convex reformulation by use of relaxations

Many combinatorial optimization problems can be formulated as the minimization of a 0-1 quadratic function subject to linear constraints. In this paper, we are interested in the exact solution of this problem through a two-phase general scheme. The first phase consists in reformulating the initial problem either into a compact mixed integer linear program or into a 0-1 quadratic convex program....

A Penalized Quadratic Convex Reformulation Method for Random Quadratic Unconstrained Binary Optimization

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...

Solving Quadratic ( 0 ; 1 ) - Problems by Semide nite Programs andCutting

Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method

Let (QP) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear equality constraints. In this paper, we present QCR, a general method to reformulate (QP) into an equivalent 0-1 program with a convex quadratic objective function. The reformulated problem can then be efficiently solved by a classical branch-and-bound algorithm, based on continuous relaxatio...