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DC decomposition based branch-and-bound algorithms for box-constrained quadratic programs

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Abstract

The difference-of-convex (DC) decomposition is an effective method for designing a branch-and-bound algorithm. In this paper, we design two new branch-and-bound algorithms based on DC decomposition, to find global solutions of nonconvex box-constrained quadratic programming problems, and compare the efficiency of the proposed algorithms with two previous state-of-the-art branch-and-bound algorithms. Numerical experiments are conducted to show the competitiveness of the proposed algorithms on 20–60 dimensional box-constrained quadratic programming problems.

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Notes

  1. The idea of using an iterative procedure is motivated by the works in [5, 15].

  2. Available at https://github.com/sburer/QUADPROGBB.

  3. Available at http://sburer.github.io/files/Box-QP.tar.gz.

  4. The BARON solver is called via the interface provided on the NEOS Server [10]. However, we believe that the significant difference of the performances between CP-BB and BARON is mainly due to algorithmic design, rather than the hardware of the machines.

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Authors and Affiliations

  1. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Cheng Lu

  2. School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China

    Zhibin Deng

  3. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, 100190, China

    Zhibin Deng

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  1. Cheng Lu
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  2. Zhibin Deng
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Correspondence to Zhibin Deng.

Additional information

Lu’s research has been supported by National Natural Science Foundation of China Grant No. 11701177, Fundamental Research Funds for the Central Universities Grant No. 2017MS058. Deng’s research has been supported by National Natural Science Foundation of China Grant No. 11501543, and Research Foundation of UCAS Grants Nos. Y65201VY00 and Y65302V1G4.

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Lu, C., Deng, Z. DC decomposition based branch-and-bound algorithms for box-constrained quadratic programs. Optim Lett 12, 985–996 (2018). https://doi.org/10.1007/s11590-017-1203-0

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