A new proximal gradient method for solving mixed variational inequality problems with a novel explicit stepsize and applications

Pham Thi Hoai

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 229, issue C, 594-610

Abstract: In this paper, we propose a new algorithm for solving monotone mixed variational inequality problems in real Hilbert spaces based on proximal gradient method. Our new algorithm uses a novel explicit stepsize which is proved to be increasing to a positive value. This property plays an important role in improving the speed of the algorithm. To the best of our knowledge, it is the first time such a kind of stepsize has been proposed for the proximal gradient method solving mixed variational inequality problems. We prove the weak convergence and strong convergence with R-linear rate of our new algorithm under standard assumptions. The reported numerical simulations for applications in sparse logistic regression and image deblurring reveal the significant efficacy performance of our proposed method compared to the recent ones.

Keywords: Proximal gradient method; Mixed variational inequality; Composite optimization model; Sparse logistic regression; Image deblurring problem (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:229:y:2025:i:c:p:594-610

DOI: 10.1016/j.matcom.2024.10.008

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