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| An Efficient Hybrid Conjugate Gradient Method for Large-Scale Nonlinear Equations with Applications in Compressive Sensing |
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| KeyWord:Conjugate gradient method, projection method, descent direction, global convergence, nonlinear equation |
| Author Name | Affiliation | | Youcef Elhamam Hemici | Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 Ferhat Abbas University, 19000, Algeria | | Samia Khelladi | Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 Ferhat Abbas University, 19000, Algeria | | Djamel Benterki | Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif 1 Ferhat Abbas University, 19000, Algeria |
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| Abstract: |
| We propose a new method to solve large-scale nonlinear monotone equations with convex constraints. The method combines the hybrid RMILHS for solving unconstrained optimization problems, with the projection technique of Solodov and Svaiter. The proposed method does not require storing large matrices, making it suitable for solving large-scale nonsmooth problems. We prove the global convergence under certain conditions. Numerical experiments show the effectiveness of the proposed algorithm, particularly in applications such as compressive sensing. |
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