A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing

In this paper, based on the three-term conjugate gradient projection method and the inertial technique, we propose a modified inertial three-term conjugate gradient projection method for solving nonlinear monotone equations with convex constraints. Embedding the inertial extrapolation step in the de...

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Published in:	Numerical algorithms Vol. 92; no. 3; pp. 1621 - 1653
Main Authors:	Ma, Guodong, Jin, Jiachen, Jian, Jinbao, Yin, Jianghua, Han, Daolan
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.03.2023 Springer Nature B.V
Subjects:	Algebra Algorithms Computer Science Conjugate gradient method Constraints Convergence Hilbert space Image restoration Mathematical analysis Methods Nonlinear equations Numeric Computing Numerical Analysis Optimization Original Paper Random variables Robustness (mathematics) Theory of Computation Linear convergence rate 68U10 65K05 Three-term conjugate gradient projection algorithm 90C56 Inertial method Compressed sensing
ISSN:	1017-1398, 1572-9265
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Abstract	In this paper, based on the three-term conjugate gradient projection method and the inertial technique, we propose a modified inertial three-term conjugate gradient projection method for solving nonlinear monotone equations with convex constraints. Embedding the inertial extrapolation step in the design for the search direction, the resulting direction satisfies the sufficient descent property which is independent of any line search rules. The global convergence and Q-linear convergence rate of the proposed algorithm are established under standard conditions. Numerical comparisons with three existing methods demonstrate that the proposed algorithm possesses superior numerical performance and good robustness for solving large-scale equations. Finally, the proposed method is applied to solve the sparse signal problems and image restoration in compressed sensing.
AbstractList	In this paper, based on the three-term conjugate gradient projection method and the inertial technique, we propose a modified inertial three-term conjugate gradient projection method for solving nonlinear monotone equations with convex constraints. Embedding the inertial extrapolation step in the design for the search direction, the resulting direction satisfies the sufficient descent property which is independent of any line search rules. The global convergence and Q-linear convergence rate of the proposed algorithm are established under standard conditions. Numerical comparisons with three existing methods demonstrate that the proposed algorithm possesses superior numerical performance and good robustness for solving large-scale equations. Finally, the proposed method is applied to solve the sparse signal problems and image restoration in compressed sensing.
Author	Jin, Jiachen Yin, Jianghua Han, Daolan Ma, Guodong Jian, Jinbao
Author_xml	– sequence: 1 givenname: Guodong surname: Ma fullname: Ma, Guodong organization: College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University – sequence: 2 givenname: Jiachen surname: Jin fullname: Jin, Jiachen organization: College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University – sequence: 3 givenname: Jinbao orcidid: 0000-0001-8048-7397 surname: Jian fullname: Jian, Jinbao email: jianjb@gxu.edu.cn organization: College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University – sequence: 4 givenname: Jianghua surname: Yin fullname: Yin, Jianghua organization: College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University – sequence: 5 givenname: Daolan surname: Han fullname: Han, Daolan organization: College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi Minzu University
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Snippet	In this paper, based on the three-term conjugate gradient projection method and the inertial technique, we propose a modified inertial three-term conjugate...
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SubjectTerms	Algebra Algorithms Computer Science Conjugate gradient method Constraints Convergence Hilbert space Image restoration Mathematical analysis Methods Nonlinear equations Numeric Computing Numerical Analysis Optimization Original Paper Random variables Robustness (mathematics) Theory of Computation
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Title	A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing
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