A Family of Modified Spectral Projection Methods for Nonlinear Monotone Equations with Convex Constraint

Zhensheng Yu, Lin Li and Peixin Li

Mathematical Problems in Engineering, 2020, vol. 2020, 1-16

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

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:2018243

DOI: 10.1155/2020/2018243

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