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Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications

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  • Davood Hajinezhad

    (Iowa State University)

  • Qingjiang Shi

    (Nanjing University of Aeronautics and Astronautics)

Abstract

In this paper, we study a class of nonconvex nonsmooth optimization problems with bilinear constraints, which have wide applications in machine learning and signal processing. We propose an algorithm based on the alternating direction method of multipliers, and rigorously analyze its convergence properties (to the set of stationary solutions). To test the performance of the proposed method, we specialize it to the nonnegative matrix factorization problem and certain sparse principal component analysis problem. Extensive experiments on real and synthetic data sets have demonstrated the effectiveness and broad applicability of the proposed methods.

Suggested Citation

  • Davood Hajinezhad & Qingjiang Shi, 2018. "Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications," Journal of Global Optimization, Springer, vol. 70(1), pages 261-288, January.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:1:d:10.1007_s10898-017-0594-x
    DOI: 10.1007/s10898-017-0594-x
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    References listed on IDEAS

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    Cited by:

    1. Dolgopolik, Maksim V., 2021. "The alternating direction method of multipliers for finding the distance between ellipsoids," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. 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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    4. Temadher A. Almaadeed & Saeid Ansary Karbasy & Maziar Salahi & Abdelouahed Hamdi, 2022. "On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 246-264, July.

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