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

被引：10

作者：

Ahookhosh, Masoud ^{[1
]}

Hien, Le Thi Khanh ^{[2
]}

Gillis, Nicolas ^{[2
]}

Patrinos, Panagiotis ^{[3
]}

机构：

[1] Univ Antwerp, Dept Math, Middelheimlaan 1, B-2020 Antwerp, Belgium

[2] Univ Mons, Fac Polytech, Dept Math & Operat Res, Rue Houdain 9, B-7000 Mons, Belgium

[3] Dept Elect Engn ESAT STADIUS KU Leuven, Kasteelpk Arenberg 10, B-3001 Leuven, Belgium

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2021年 / 190卷 / 01期

基金：

欧盟地平线“2020”;

关键词：

Nonsmooth nonconvex optimization; Block Bregman proximal algorithm; Inertial effects; Block relative smoothness; Symmetric nonnegative matrix tri-factorization; ALTERNATING LINEARIZED MINIMIZATION; CONVEX-OPTIMIZATION; 1ST-ORDER METHODS; DESCENT METHODS; CONVERGENCE;

D O I：

10.1007/s10957-021-01880-5

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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-Lojasiewicz (KL) property. We also provide the convergence rate when a regularization of the objective function satisfies the Lojasiewicz 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.

引用

页码：234 / 258

页数：25

共 54 条

[1]

Ahookhosh M., COMPUT OPTIM APPL, P1, DOI [10.1007/s10589-021-00286-3(2021, DOI 10.1007/S10589-021-00286-3(2021]

[2] A BREGMAN FORWARD-BACKWARD LINESEARCH ALGORITHM FOR NONCONVEX COMPOSITE OPTIMIZATION: SUPERLINEAR CONVERGENCE TO NONISOLATED LOCAL MINIMA [J].

Ahookhosh, Masoud ;

Themelis, Andreas ;

Patrinos, Panagiotis .

SIAM JOURNAL ON OPTIMIZATION, 2021, 31 (01) :653-685

[3] Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity [J].

Ahookhosh, Masoud .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2019, 89 (03) :319-353

[4]

Airoldi EM, 2008, J MACH LEARN RES, V9, P1981

[5] A new class of alternating proximal minimization algorithms with costs-to-move [J].

Attouch, H. ;

Redont, P. ;

Soubeyran, A. .

SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (03) :1061-1081

[6] On the convergence of the proximal algorithm for nonsmooth functions involving analytic features [J].

Attouch, Hedy ;

Bolte, Jerome .

MATHEMATICAL PROGRAMMING, 2009, 116 (1-2) :5-16

[7] Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods [J].

Attouch, Hedy ;

Bolte, Jerome ;

Svaiter, Benar Fux .

MATHEMATICAL PROGRAMMING, 2013, 137 (1-2) :91-129

[8] Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality [J].

Attouch, Hedy ;

Bolte, Jerome ;

Redont, Patrick ;

Soubeyran, Antoine .

MATHEMATICS OF OPERATIONS RESEARCH, 2010, 35 (02) :438-457

[9]

Auslender A, 1976, OPTIMISATION METHODE

[10]

Bauschke H.H., 2017, CMS Books Math./Ouvrages Math. SMC, V2, DOI DOI 10.1007/978-3-319-48311-5

← 1 2 3 4 5 6 →