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Mathematics
Volume 13
Issue 12
10.3390/math13121966
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Article

Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces

by
Chih-Sheng Chuang
Department of Applied Mathematics, National Chiayi University, Chiayi 600355, Taiwan
Mathematics 2025, 13(12), 1966; https://doi.org/10.3390/math13121966 (registering DOI)
Submission received: 20 May 2025 / Revised: 10 June 2025 / Accepted: 13 June 2025 / Published: 14 June 2025
(This article belongs to the Section C: Mathematical Analysis)
Versions Notes

Abstract

The inverse mixed variational inequality problem comes from classical variational inequality, and it has many applications. In this paper, we propose new algorithms to study the inverse mixed variational inequality problems in Hilbert spaces, and these algorithms are based on the generalized projection operator. Next, we establish convergence theorems under inverse strong monotonicity conditions. In addition, we also provide inertial-type algorithms for the inverse mixed variational inequality problems with conditions that differ from the above convergence theorems.
Keywords: variational inequality; inverse variational inequality; inverse strong monotonicity; inertial algorithm; generalized projection variational inequality; inverse variational inequality; inverse strong monotonicity; inertial algorithm; generalized projection

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MDPI and ACS Style

Chuang, C.-S. Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces. Mathematics 2025, 13, 1966. https://doi.org/10.3390/math13121966

AMA Style

Chuang C-S. Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces. Mathematics. 2025; 13(12):1966. https://doi.org/10.3390/math13121966

Chicago/Turabian Style

Chuang, Chih-Sheng. 2025. "Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces" Mathematics 13, no. 12: 1966. https://doi.org/10.3390/math13121966

APA Style

Chuang, C.-S. (2025). Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces. Mathematics, 13(12), 1966. https://doi.org/10.3390/math13121966

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