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Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization

Author

Listed:
  • Masoud Ahookhosh

    (University of Antwerp)

  • Le Thi Khanh Hien

    (Université de Mons. Rue de Houdain 9)

  • Nicolas Gillis

    (Université de Mons. Rue de Houdain 9)

  • Panagiotis Patrinos

    (KU Leuven)

Abstract

We introduce and analyze BPALM and A-BPALM, two multi-block proximal alternating linearized minimization algorithms using Bregman distances for solving structured nonconvex problems. The objective function is the sum of a multi-block relatively smooth function (i.e., relatively smooth by fixing all the blocks except one) and block separable (nonsmooth) nonconvex functions. The sequences generated by our algorithms are subsequentially convergent to critical points of the objective function, while they are globally convergent under the KL inequality assumption. Moreover, the rate of convergence is further analyzed for functions satisfying the Łojasiewicz’s gradient inequality. We apply this framework to orthogonal nonnegative matrix factorization (ONMF) that satisfies all of our assumptions and the related subproblems are solved in closed forms, where some preliminary numerical results are reported.

Suggested Citation

  • Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization," Computational Optimization and Applications, Springer, vol. 79(3), pages 681-715, July.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00286-3
    DOI: 10.1007/s10589-021-00286-3
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    2. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.

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