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Preconditioned ADMM for a Class of Bilinear Programming Problems

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  • Xiaobo Liang
  • Jianchao Bai

Abstract

We design a novel preconditioned alternating direction method for solving a class of bilinear programming problems, where each subproblem is solved by adding a positive-definite regularization term with a proximal parameter. By the aid of the variational inequality, the global convergence of the proposed method is analyzed and a worst-case convergence rate in an ergodic sense is established. Several preliminary numerical examples, including the Markowitz portfolio optimization problem, are also tested to verify the performance of the proposed method.

Suggested Citation

  • Xiaobo Liang & Jianchao Bai, 2018. "Preconditioned ADMM for a Class of Bilinear Programming Problems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, January.
    • Handle: RePEc:hin:jnlmpe:5694201
    DOI: 10.1155/2018/5694201
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    Cited by:

    1. Zhiqing Meng & Min Jiang & Rui Shen & Leiyan Xu & Chuangyin Dang, 2021. "An objective penalty function method for biconvex programming," Journal of Global Optimization, Springer, vol. 81(3), pages 599-620, November.

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