A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES*

doi:10.1007/s10473-023-0112-9

摘要/Abstract

摘要： In this paper, we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving this problem, we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method. Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in [0; 1]. The purpose of this work is to continue working in this direction, we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be $1$. Under suitable mild conditions, we establish the weak convergence of the proposed algorithm. Moreover, linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions. Finally, some numerical illustrations are given to confirm the theoretical analysis.

关键词: subgradient extragradient method, inertial method, variational inequality problem, pseudomonotone mapping, strong convergence, convergence rate

Abstract: In this paper, we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving this problem, we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method. Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in [0; 1]. The purpose of this work is to continue working in this direction, we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be $1$. Under suitable mild conditions, we establish the weak convergence of the proposed algorithm. Moreover, linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions. Finally, some numerical illustrations are given to confirm the theoretical analysis.

Key words: subgradient extragradient method, inertial method, variational inequality problem, pseudomonotone mapping, strong convergence, convergence rate

Duong Viet Thong, Vu Tien Dung. A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES^*[J]. 数学物理学报(英文版), 2023, 43(1): 184-204.

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A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES^*

A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES^*

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