Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the ℓ1-norm regularized minimization problem.
|Number of pages||18|
|Journal||Japan Journal of Industrial and Applied Mathematics|
|Publication status||Published - Sept 2021|
- Conjugate gradient
- Image restoration
- Nonlinear equations
- Projection method