A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint. (28th October 2020)

• Record Type: Journal Article
• Authors: Yu, Zhensheng; Li, Lin; Li, Peixin
• Other Names: Dulikravich George S. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-10-28
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/2018243
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 ℓ 1 -norm regularization problem in compressive sensing demonstrate the efficiency and efficacy of our method.