A derivative-free RMIL conjugate gradient method for constrained nonlinear systems of monotone equations

Xiaowei Fang; Xiaowei Fang

doi:10.3934/math.2025528

AIMS Mathematics

2025, Volume 10, Issue 5: 11656-11675. doi: 10.3934/math.2025528

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Research article

A derivative-free RMIL conjugate gradient method for constrained nonlinear systems of monotone equations

Xiaowei Fang ^,

Department of Mathematics, Huzhou University, Huzhou Zhejiang, 313000, China

Received: 16 March 2025 Revised: 06 May 2025 Accepted: 12 May 2025 Published: 21 May 2025
MSC : 90C56, 90C30

In this paper, we introduce a derivative-free RMIL conjugate gradient method designed for nonlinear systems of monotone equations with convex constraints. The proposed method represents a refinement of the RMIL method through its integration with projection techniques and a derivative-free line search strategy. When certain reasonable assumptions are satisfied, we can prove the global convergence of the proposed method. Numerical experiments demonstrate that the method is highly effective. Moreover, we employ the method to solve sparse signal restoration problems.
- nonlinear monotone equations,
- conjugate gradient method,
- hyperplane projection technique,
- signal recovery
Citation: Xiaowei Fang. A derivative-free RMIL conjugate gradient method for constrained nonlinear systems of monotone equations[J]. AIMS Mathematics, 2025, 10(5): 11656-11675. doi: 10.3934/math.2025528

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Abstract

In this paper, we introduce a derivative-free RMIL conjugate gradient method designed for nonlinear systems of monotone equations with convex constraints. The proposed method represents a refinement of the RMIL method through its integration with projection techniques and a derivative-free line search strategy. When certain reasonable assumptions are satisfied, we can prove the global convergence of the proposed method. Numerical experiments demonstrate that the method is highly effective. Moreover, we employ the method to solve sparse signal restoration problems.

References

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