Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM FOR SDP RELAXATION OF THE BINARY QUADRATIC PROGRAMMING

  • MU XUEWEN (DEPARTMENT OF APPLIED MATHEMATICS, XIDIAN UNIVERSITY) ;
  • LID SANYANG (DEPARTMENT OF APPLIED MATHEMATICS, XIDIAN UNIVERSITY) ;
  • ZHANG YALING (DEPARTMENT OF COMPUTER SCIENCE AND TECHNOLOGY, XI'AN UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Published : 2005.11.01
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Abstract

In this paper, we obtain a successive quadratic programming algorithm for solving the semidefinite programming (SDP) relaxation of the binary quadratic programming. Combining with a randomized method of Goemans and Williamson, it provides an efficient approximation for the binary quadratic programming. Furthermore, its convergence result is given. At last, We report some numerical examples to compare our method with the interior-point method on Maxcut problem.

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References

  1. F. Barahon and M. Grotschel, An application of combinatorial optimization to statiscal optimization and circuit layout design, Oper. Res. 36 (1998), no. 3, 493-513 https://doi.org/10.1287/opre.36.3.493
  2. K. C. Chang and D. H., Eifficient algorithms for layer assignment problems, IEEE Trans. on Computer Aided Design. CAD-6 (1987), no. 1, 67-78
  3. R. Chen, A graph theoretic via minimization algorithm for teo layer printed circuit boards, IEEE Trans. Circuits Systems CAS 30 (1983), no. 5, 284-299 https://doi.org/10.1109/TCS.1983.1085357
  4. M. X. Goeman and D. P. Williamson, Improved approximation algorithms for maximum cut and satisfiably problem using semidefinite programming, J. ACM 42 (1995), 1115-1145 https://doi.org/10.1145/227683.227684
  5. S. Benson, Y. Ye, and X. Zhang, Solving large scale sprase semidefinite programming for combinatorial optimization, SIAM J. Optim. 10 (2000), no. 2, 443-461 https://doi.org/10.1137/S1052623497328008
  6. C. Helberg and F. Rendel, An interior point method for semidefinite programming, SIAM J. Optim. 10 (1990), 842-861
  7. C. Helberg and F. Rendl, A spectral bundle method for semidefinite programing, SIAM J. Optim. 10 (2000), 673-696 https://doi.org/10.1137/S1052623497328987
  8. M. Peinadoo and S. Homer, Design and performance of parallel and distributed approximation algorithms for max-cut, Journal of Parallel and Distributed Computing. 9 (1998), 141-160
  9. S. Burer and R. D. C. Monteriro, A projected gradient algorithm for solving the max-cut relaxation, Optim. Methods Softw. 15 (2001), 175-200 https://doi.org/10.1080/10556780108805818
  10. M. Marko, Makeka, and Pekka Neittaanmaki, Nonsmooth optimization: analysis and algorithms with application to optimization control, World scientific, Singapore, 1992
  11. C. Helmberg, Semidefinite programming for combinatorial optimization, Konrad- Zuse-Zentrum fur informationstechnik Berlin, Germany, 2000
  12. M. V. Nayakakuppam, M. L. Overton, and S. Schemita, SDPpack user's guide- version 0.9 Beta, Technical Report Yr 1997-737, Courtant Institute of Mathematical Science, NYU, New York, NY, 1997