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Journal of Applied Mathematics and Computing

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13-12-2023 | Original Research

A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications

Authors: Guodong Ma, Liqi Liu, Jinbao Jian, Xihong Yan

Published in: Journal of Applied Mathematics and Computing | Issue 1/2024

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Abstract

The conjugate gradient projection method (CGPM) has good theoretical properties and numerical performance for solving large-scale nonlinear monotone equations with convex constraints. In this paper, by designing a modified adaptive line search, a new hybrid CGPM-based algorithm is proposed. The search direction satisfies the sufficient descent and trust region properties which are independent of the choices of the line search. The global convergence of the algorithm is analyzed without the Lipschitz continuity. The linear convergence rate is established under some appropriate assumptions. Some preliminary numerical experiment results are reported, which show that our proposed algorithm is promising. Finally, the proposed algorithm is extended to solve the sparse signal and image restoration problems in compressed sensing.

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Title: A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications
Authors: Guodong Ma
Liqi Liu
Jinbao Jian
Xihong Yan
Publication date: 13-12-2023
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1/2024
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-023-01960-x

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