Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 963563, 7 pages.

A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming

Xuewen Mu and Yaling Zhang

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Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given. Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report some numerical examples to compare our algorithm with randomized algorithm based on the interior point method and the feasible direction algorithm on max-cut problem. Simulation results have shown that our method is faster than the other two methods.

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J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 963563, 7 pages.

First available in Project Euclid: 14 March 2014

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Mu, Xuewen; Zhang, Yaling. A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming. J. Appl. Math. 2013, Special Issue (2013), Article ID 963563, 7 pages. doi:10.1155/2013/963563.

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