A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint
Joint Authors
Yu, Zhensheng
Li, Peixin
Li, Lin
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-10-28
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
In this paper, we propose a family of modified spectral projection methods for nonlinear monotone equations with convex constraints, where the spectral parameter is mainly determined by a convex combination of the modified long Barzilai–Borwein stepsize and the modified short Barzilai–Borwein stepsize.
We obtain a trial point by the spectral method and then get the iteration point by the projection technique.
The algorithm can generate a bounded iterative sequence automatically, and we obtain the global convergence of the proposed method in the sense that every limit point is a solution of the nonlinear equation.
The proposed method can be used to resolve the large-scale nonlinear monotone equations with convex constraints including smooth and nonsmooth equations.
Numerical results for nonlinear equation problems and the ℓ1-norm regularization problem in compressive sensing demonstrate the efficiency and efficacy of our method.
American Psychological Association (APA)
Yu, Zhensheng& Li, Lin& Li, Peixin. 2020. A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1193651
Modern Language Association (MLA)
Yu, Zhensheng…[et al.]. A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint. Mathematical Problems in Engineering No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1193651
American Medical Association (AMA)
Yu, Zhensheng& Li, Lin& Li, Peixin. A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1193651
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193651