Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces
Abstract
1. Introduction
- (i)
- The classical algorithm for the inverse mixed variational inequality problem:
- (ii)
- A generalized algorithm from the classical algorithm:
- (iii)
- Inertial Algorithm (1):, , and are positive real numbers, is a sequence in the interval .
- (iv)
- Inertial Algorithm (2):
2. Preliminaries
- (i)
- B is monotone if for all ;
- (ii)
- B is β-strongly monotone if for all ;
- (iii)
- B is β-inverse strongly monotone if for all .
- (i)
- T is a nonexpansive mapping if for every ;
- (ii)
- T is a firmly nonexpansive mapping if for every , that is, for every ;
- (iii)
- is quasi-nonexpansive mapping if and for all and .
- (i)
- for each , the set is nonempty and singleton.
- (ii)
- for each , if, and only if,
- (iii)
- is a firmly nonexpansive mapping.
3. Algorithms for the Inverse Mixed Variational Inequality Problem
4. Inertial Algorithms for the Inverse Mixed Variational Inequality Problem
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
IVI | Inverse variational inequality problem |
IMVI | Inverse mixed variational inequality problem |
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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
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 StyleChuang, 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 StyleChuang, 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