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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Veröffentlicht in:Numerical algorithms Jg. 92; H. 3; S. 1621 - 1653
Hauptverfasser: Ma, Guodong, Jin, Jiachen, Jian, Jinbao, Yin, Jianghua, Han, Daolan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.03.2023
Springer Nature B.V
Schlagworte:
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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01356-1