A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization

Masoud Ahookhosh (), Le Thi Khanh Hien (), Nicolas Gillis () and Panagiotis Patrinos ()
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Masoud Ahookhosh: University of Antwerp
Le Thi Khanh Hien: Université de Mons
Nicolas Gillis: Université de Mons
Panagiotis Patrinos: Department of Electrical Engineering (ESAT-STADIUS) – KU Leuven

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 1, No 10, 234-258

Abstract: Abstract We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We show that the cluster points of the sequence generated by BIBPA are critical points of the objective under standard assumptions, and this sequence converges globally when a regularization of the objective function satisfies the Kurdyka-Łojasiewicz (KL) property. We also provide the convergence rate when a regularization of the objective function satisfies the Łojasiewicz inequality. We apply BIBPA to the symmetric nonnegative matrix tri-factorization (SymTriNMF) problem, where we propose kernel functions for SymTriNMF and provide closed-form solutions for subproblems of BIBPA.

Keywords: Nonsmooth nonconvex optimization; Block Bregman proximal algorithm; Inertial effects; Block relative smoothness; Symmetric nonnegative matrix tri-factorization; 90C06; 90C25; 90C26; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-021-01880-5

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