Block coordinate descentwith time perturbation for nonconvex nonsmooth problems in real-world studies

Liu, Rui; Sun, Weichu; Hou, Tao; Hu, Chunhong; Qiao, Linbo

doi:10.1631/fitee.1900341

Cited by 2 publications

(2 citation statements)

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“…With an alternating minimization strategy, a forward-backward algorithm was proposed in [15], and the corresponding sequence is proved to be convergent to a stationary point of the considered problem. The authors in [30] came up with a original parallel block coordinate descent method, which can effectively avoid the generation of saddle points and sub-optimal points. And the authors in [30] also verified the efficacy of the proposed algorithm by some numerical experiments on practical application problems.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in [30] came up with a original parallel block coordinate descent method, which can effectively avoid the generation of saddle points and sub-optimal points. And the authors in [30] also verified the efficacy of the proposed algorithm by some numerical experiments on practical application problems. In particular, only the separable part is required to be smooth in [25], which is different from the above literatures in which the nonseparable part is required to be smooth.…”

Section: Introductionmentioning

confidence: 99%

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Smoothing Randomized Block-coordinate Proximal Gradient Algorithms for Nonsmooth Nonconvex Composite Optimization

Bian

2023

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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 and one of which is separable. The pivotal tool of our analysis is the connection of the proximal gradient mapping with V-proximal mapping and Bregman proximal mapping. S-RBCPG algorithm overcome the non-smoothness issue of the objective function by utilizing the smoothing technique and we establish its subsequential convergence. Further, B-RBCPG algorithm is designed for cases where the separable function is separately relative smooth (that is, each separation part is relative smooth). Then, we establish the global convergence and R-linear convergence rate of the B-RBCPG algorithm under expectation by assuming the Kurdyka-Łojasiewicz property on the objective function without any convexity assumption. Finally, we use numerical experiments to illustrate the effectiveness and convergence of the proposed algorithms. MSC Classification: 90C30 , 90C26 , 65K05

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Section: Introductionmentioning

confidence: 99%