An inertial Popov's method for solving pseudomonotone variational inequalities
type: Item
instance of: scholarly article
title: An inertial Popov's method for solving pseudomonotone variational inequalities
zbMATH Open document ID: 1473.49003
author: Duong Viet Thong
author: Xiao-Huan Li
author: Qiao-Li Dong
author: Yeol Je Cho
author: Themistocles M. Rassias
published in: Optimization Letters
publication date: 2021-05-05T00:00:00Z
review text: In this paper, the authors present a new method to solve a variational inequality problem in Hilbert spaces. The method is modified from the traditional Popov's extragradient method using an inertial parameter. One of the major advantages of the proposed method is that only one value of the inequality mapping and one projection onto the admissible set per one iteration is computed. Furthermore, the requirement of prior knowledge of the Lipschitz constants of the variational inequality mapping is also relaxed. The goal is to accelerate the traditional Popov's algorithm. The authors present results on weak convergence of the proposed algorithm under pseudomonotonicity and Lipschitz continuity of the associated mapping. A section on numerical experiments validate the theoretical results. The theoretical results in the papaer are well presented and easy to follow. The proposed algorithm is certainly new in context of solving variational inequality problems. However, a couple of drawbacks of the paper are: first, the introduction primarily consists of standard definitions and notations rather than focusing on the major drawbacks of existing methods and highlighting the novelty of the proposed algorithm. For e.g., Popov's method, which is the basis of this work, and its motivation and significance is not described clearly. Second, the authors state in the abstract that their theoretical results generalize some well-known results in literature. It is not clear from the introduction and the body of the paper which results are being generalized. These two drawbacks lessen the impact of this important work.
reviewed by: Souvik Roy
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 7343979
zbMATH Keywords: Popov's method
zbMATH Keywords: variational inequality problem
zbMATH Keywords: pseudo-monotone mapping
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
full work available at URL: s11590-020-01599-8
OpenAlex ID: W3027232935
cites work: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
cites work: Q4145166
cites work: On the \(O(1/t)\) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators
cites work: The subgradient extragradient method for solving variational inequalities in Hilbert space
cites work: Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space
cites work: Hybrid approximate proximal method with auxiliary variational inequality for vector optimization
cites work: Iterative methods for fixed point problems in Hilbert spaces
cites work: Pseudo-monotone complementarity problems in Hilbert space
cites work: Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators
cites work: Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery
cites work: The projection and contraction methods for finding common solutions to variational inequality problems
cites work: Finite-Dimensional Variational Inequalities and Complementarity Problems
cites work: Q5335941
cites work: Q5523516
cites work: Q3322631
cites work: Q5146236
cites work: A new low-cost double projection method for solving variational inequalities
cites work: New extragradient-like algorithms for strongly pseudomonotone variational inequalities
cites work: Korpelevich's method for variational inequality problems in Banach spaces
cites work: A variant of korpelevich’s method for variational inequalities with a new search strategy
cites work: Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces
cites work: A New Extragradient Method for Strongly Pseudomonotone Variational Inequalities
cites work: Combined relaxation methods for variational inequalities
cites work: Q4110807
cites work: Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces
cites work: Inertial iterative process for fixed points of certain quasi-nonexpansive mappings
cites work: A Hybrid Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems
cites work: An extragradient algorithm for monotone variational inequalities
cites work: Projected Reflected Gradient Methods for Monotone Variational Inequalities
cites work: A hybrid method without extrapolation step for solving variational inequality problems
cites work: Low-cost modification of Korpelevich's methods for monotone equilibrium problems
cites work: Some methods of speeding up the convergence of iteration methods
cites work: Q3905081
cites work: Single projection method for pseudo-monotone variational inequality in Hilbert spaces
cites work: A New Projection Method for Variational Inequality Problems
cites work: Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces
cites work: Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities
cites work: On the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities
cites work: Strong convergence result for solving monotone variational inequalities in Hilbert space
cites work: A modified projected gradient method for monotone variational inequalities
cites work: Convergence of a subgradient extragradient algorithm for solving monotone variational inequalities
DOI: 10.1007/S11590-020-01599-8
description: scientific article; zbMATH DE number 7343979