Smoothing randomized block-coordinate proximal gradient algorithms for nonsmooth nonconvex composite optimization

In this paper, we propose a smoothing randomized block-coordinate proximal gradient (S-RBCPG) algorithm and a Bregman randomized block-coordinate proximal gradient (B-RBCPG) algorithm for minimizing the sum of two nonconvex nonsmooth functions, one of which is block separable. The pivotal tool of ou...

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Veröffentlicht in:Numerical algorithms Jg. 100; H. 1; S. 395 - 424
Hauptverfasser: Li, Xue, Bian, Wei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2025
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Computer Science
Convergence
Inverse problems
Machine learning
Mapping
Numeric Computing
Numerical Analysis
Optimization
Smoothing
Smoothness
Theory of Computation
Kurdyka-Łojasiewicz property
90C30
65K05
Relative smoothness
Block-coordinate
90C26
Smoothing method
Nonsmooth nonconvex optimization
ISSN:1017-1398, 1572-9265
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Zusammenfassung:In this paper, we propose a smoothing randomized block-coordinate proximal gradient (S-RBCPG) algorithm and a Bregman randomized block-coordinate proximal gradient (B-RBCPG) algorithm for minimizing the sum of two nonconvex nonsmooth functions, one of which is block separable. The pivotal tool of our analysis is the connection of the proximal gradient mapping with V-proximal mapping and Bregman proximal mapping. The S-RBCPG algorithm overcomes the non-smoothness of the objective function by utilizing the smoothing technique and we establish its subsequential convergence. Further, the B-RBCPG algorithm is designed for the case where the separable function is relatively smooth (that is, each separation part is relatively smooth). Then, we establish the R -linear convergence rate of the B-RBCPG algorithm under expectation by assuming the Kurdyka-Łojasiewicz property on the objective function. Finally, we use some numerical experiments to illustrate the effectiveness and convergence of the proposed algorithms.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01965-y