Analysis of versions of relaxed inertial projection and contraction method

Shehu, Yekini; Liu, Lulu; Mu, Xuewen; Dong, Qiao-Li

doi:10.1016/j.apnum.2021.02.004

Cited by 18 publications

(2 citation statements)

References 28 publications

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“…However, any inertial algorithm with Bregman distance is only applicable for inertial algorithms based on hybrid projection method and shrinking projection method due to structure of Bregman distance and the inertial term in such algorithms. In the past few years, various inertial algorithms have been studied and developed for solving many kinds of optimization problems (see, e.g., previous studies [29][30][31][32][33][34][35][36][37]). The following questions arise from the results mentioned above:…”

Section: Introductionmentioning

confidence: 99%

Inertial‐like Bregman projection method for solving systems of variational inequalities

Jolaoso

Pholasa

Sunthrayuth

et al. 2023

Math Methods in App Sciences

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In this paper, we propose a self‐adaptive inertial‐like algorithm with Bregman distance for approximating a common solution of systems of variational inequalities for a class of monotone and Lipschitz continuous mappings in real reflexive Banach spaces. Our algorithm is constructed without using hybrid projection method and shrinking projection method, and its strong convergence is proved without the prior information of the Lipschitz constant of the mapping. Finally, we provide some numerical experiments to illustrate the performance of the newly proposed method including a comparison with related works in solving signal restoration problems.

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Section: Introductionmentioning

confidence: 99%

Inertial‐like Bregman projection method for solving systems of variational inequalities

Jolaoso

Pholasa

Sunthrayuth

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…On the other hand, in order to accelerate the convergence, the inertial methods have been studied extensively by many scholars [5][6][7][8][9][10][11][12]. One of the important results is the inertial Mann algorithm which is introduced by Maingé [5] in 2007:…”

Section: Introductionmentioning

confidence: 99%