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An augmented Lagrangian method for binary quadratic programming based on a class of continuous functions

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Abstract

In this paper, an augmented Lagrangian method is proposed for binary quadratic programming (BQP) problems based on a class of continuous functions. The binary constraints are converted into a class of continuous functions. The approach reformulates the BQP problem as an equivalent augmented Lagrangian function, and then seeks its minimizer via an augmented Lagrangian method, in which the subproblem is solved by Barzilai–Borwein type method. Numerical results are reported for max-cut problem. The results indicate that the augmented Lagrangian approach is promising for large scale binary quadratic programming by the quality of the near optimal values and the low computational time.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Xuewen Mu

  2. School of Information and Communication Engineering, Dalian University of Technology, Dalian, 116024, China

    Wenlong Liu

Authors
  1. Xuewen Mu
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  2. Wenlong Liu
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Correspondence to Xuewen Mu.

Additional information

The work is supported by National Science Foundation for Young Scientists of China (No. 11101320), by the National Natural Science Foundation of China (No. 11032008, 11372069), and by China Scholarship Council (CSC). This work was conducted while the first author has been visiting Ohio University, Department of Mathematics.

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Mu, X., Liu, W. An augmented Lagrangian method for binary quadratic programming based on a class of continuous functions. Optim Lett 10, 485–497 (2016). https://doi.org/10.1007/s11590-015-0873-8

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  • DOI: https://doi.org/10.1007/s11590-015-0873-8

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