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

Xuewen Mu | Zendy; Yaling Zhang | Zendy

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

Author(s) -

Xuewen Mu,

Yaling Zhang

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/963563

Subject(s) - quadratic programming , quadratically constrained quadratic program , algorithm , mathematics , semidefinite programming , relaxation (psychology) , rank (graph theory) , binary number , second order cone programming , mathematical optimization , interior point method , sequential quadratic programming , quadratic equation , linear programming , criss cross algorithm , nonlinear programming , linear fractional programming , nonlinear system , combinatorics , psychology , social psychology , physics , geometry , arithmetic , convex optimization , regular polygon , quantum mechanics

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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