We present a new ellipsoidal relaxation of 0-1 quadratic optimization problems. The relaxation and the dual problem are derived. Both these problems are strictly feasible;so strong duality holds, and they can be solve...
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We present a new ellipsoidal relaxation of 0-1 quadratic optimization problems. The relaxation and the dual problem are derived. Both these problems are strictly feasible;so strong duality holds, and they can be solved numerically using primal-dual interior-point methods. Numerical results are presented which indicate that the described relaxation is efficient. (C) 2003 Published by Elsevier B.V.
We review various relaxations of (0,1)-quadraticprogramming problems. These include semidefinite programs, parametric trust region problems and concave quadratic maximization. All relaxations that we consider lead to...
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We review various relaxations of (0,1)-quadraticprogramming problems. These include semidefinite programs, parametric trust region problems and concave quadratic maximization. All relaxations that we consider lead to efficiently solvable problems. The main contributions of the paper are the following. Using Lagrangian duality, we prove equivalence of the relaxations in a unified and simple way. Some of these equivalences have been known previously, but our approach leads to short and transparent proofs. Moreover we extend the approach to the case of equality constrained problems by taking the squared linear constraints into the objective function. We show how this technique can be applied to the quadratic Assignment Problem, the Graph Partition Problem and the Max-Clique Problem. Finally we show our relaxation to be best possible among all quadratic majorants with zero trace.
We consider three parametric relaxations of the (0, 1)-quadraticprogramming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maxim...
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We consider three parametric relaxations of the (0, 1)-quadraticprogramming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maximum eigenvalue of a bordered matrix. When minimized over the parameter, each of the relaxations provides an upper bound on the original discrete problem. Moreover, these bounds are efficiently computable. Our main result is that, surprisingly, all three bounds are equal.
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