scholarly journals Inertial hybrid algorithm for variational inequality problems in Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Tian ◽  
Bing-Nan Jiang
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Variational Inequality Problems

scholarly journals A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 248 ◽  
Author(s):  
Suthep Suantai ◽  
Pronpat Peeyada ◽  
Damrongsak Yambangwai ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Common Solution ◽  
Line Method ◽  
The Common ◽  
Monotone Hybrid Algorithm

In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhongbing Xie ◽  
Gang Cai ◽  
Xiaoxiao Li ◽  
Qiao-Li Dong
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Tseng’S Extragradient Method

Abstract The purpose of this paper is to study a new Tseng’s extragradient method with two different stepsize rules for solving pseudomonotone variational inequalities in real Hilbert spaces. We prove a strong convergence theorem of the proposed algorithm under some suitable conditions imposed on the parameters. Moreover, we also give some numerical experiments to demonstrate the performance of our algorithm.

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