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

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  • Hoai, Pham Thi

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.

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  • Hoai, Pham Thi, 2025. "A new proximal gradient method for solving mixed variational inequality problems with a novel explicit stepsize and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 594-610.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:594-610
    DOI: 10.1016/j.matcom.2024.10.008
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    References listed on IDEAS

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    1. Jolaoso, Lateef O. & Shehu, Yekini & Yao, Jen-Chih, 2022. "Inertial extragradient type method for mixed variational inequalities without monotonicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 353-369.
    2. I. V. Konnov & E. O. Volotskaya, 2002. "Mixed variational inequalities and economic equilibrium problems," Journal of Applied Mathematics, Hindawi, vol. 2, pages 1-26, January.
    3. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.
    4. I. V. Konnov & E. O. Volotskaya, 2002. "Mixed variational inequalities and economic equilibrium problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2(6), pages 289-314.
    5. Khalid Addi & Daniel Goeleven, 2017. "Complementarity and Variational Inequalities in Electronics," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Operations Research, Engineering, and Cyber Security, pages 1-43, Springer.
    6. Hongwei Liu & Jun Yang, 2020. "Weak convergence of iterative methods for solving quasimonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 491-508, November.
    7. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
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    1. Duong Viet Thong & Vu Tien Dung & Hoang Thi Thanh Tam, 2025. "A Self Adaptive Projected Gradient Method for Solving Non-Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-27, July.

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