Experiments in quadratic 0-1 programming
Mathematical Programming: Series A and B
Probabilistic bounds and algorithms for the maximum satisfiability problem
Annals of Operations Research
Mathematical Programming: Series A and B
Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs
SIAM Journal on Optimization
Approximation of the Stability Number of a Graph via Copositive Programming
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
Discrete Applied Mathematics
Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations
Computational Optimization and Applications
LMI Approximations for Cones of Positive Semidefinite Forms
SIAM Journal on Optimization
Minimizing Polynomials via Sum of Squares over the Gradient Ideal
Mathematical Programming: Series A and B
Semidefinite representations for finite varieties
Mathematical Programming: Series A and B
The quadratic knapsack problem-a survey
Discrete Applied Mathematics
SIAM Review
An iterative scheme for valid polynomial inequality generation in binary polynomial programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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Several types of relaxations for binary quadratic polynomial programs can be obtained using linear, second-order cone, or semidefinite techniques. In this paper, we propose a general framework to construct conic relaxations for binary quadratic polynomial programs based on polynomial programming. Using our framework, we re-derive previous relaxation schemes and provide new ones. In particular, we present three relaxations for binary quadratic polynomial programs. The first two relaxations, based on second-order cone and semidefinite programming, represent a significant improvement over previous practical relaxations for several classes of nonconvex binary quadratic polynomial problems. From a practical point of view, due to the computational cost, semidefinite-based relaxations for binary quadratic polynomial problems can be used only to solve small to midsize instances. To improve the computational efficiency for solving such problems, we propose a third relaxation based purely on second-order cone programming. Computational tests on different classes of nonconvex binary quadratic polynomial problems, including quadratic knapsack problems, show that the second-order-cone-based relaxation outperforms the semidefinite-based relaxations that are proposed in the literature in terms of computational efficiency, and it is comparable in terms of bounds.