Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs.

SIAM Journal on Optimization 01/2011; 21:391-414. DOI: 10.1137/100802190
Source: DBLP

ABSTRACT techniques. In this paper, we propose a general framework to construct conic relaxations for binary quadratic polynomial programs based on polynomial programming. Using our frame- work, we re-derive previous relaxation schemes and provide new ones. In particular, we present three relax- ations for binary quadratic polynomial programs. The rst two relaxations, based on second-order cone and semidenite programming, represent a signicant improvement over previous practical relaxations for several classes of non-convex binary quadratic polynomial problems. From a practical point of view, due to the computational cost, semidenite-based relaxations for binary quadratic polynomial problems can be used only to solve small to mid-size instances. To improve the computational eciency for solving such problems, we propose a third relaxation based purely on second-order cone programming. Computational tests on dif- ferent classes of non-convex binary quadratic polynomial problems, including quadratic knapsack problems, show that the second-order cone-based relaxation outperforms the semidenite-based relaxations that are proposed in the literature in terms of computational eciency and is comparable in terms of bounds.

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