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Numerical Algorithms
Published in: Numerical Algorithms 4/2022

26-07-2021 | Original Paper

Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems

Authors: Ha Manh Linh, Simeon Reich, Duong Viet Thong, Vu Tien Dung, Nguyen Phuong Lan

Published in: Numerical Algorithms | Issue 4/2022

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Abstract

We study variational inequalities and fixed point problems in real Hilbert spaces. A new algorithm is proposed for finding a common element of the solution set of a pseudo-monotone variational inequality and the fixed point set of a demicontractive mapping. The advantage of our algorithm is that it does not require prior information regarding the Lipschitz constant of the variational inequality operator and that it only computes one projection onto the feasible set per iteration. In addition, we do not need the sequential weak continuity of the variational inequality operator in order to establish our strong convergence theorem. Next, we also obtain an R-linear convergence rate for a related relaxed inertial gradient method under strong pseudo-monotonicity and Lipschitz continuity assumptions on the variational inequality operator. Finally, we present several numerical examples which illustrate the performance and the effectiveness of our algorithm.
previous article The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations
next article An infeasible projection type algorithm for nonmonotone variational inequalities

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Metadata
Title
Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems
Authors
Ha Manh Linh
Simeon Reich
Duong Viet Thong
Vu Tien Dung
Nguyen Phuong Lan
Publication date
26-07-2021
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2022
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-021-01169-8

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