Modified optimal Perry conjugate gradient method for solving system of monotone equations with applications
The paper is devoted to large-scale monotone nonlinear equations. To solve such problems, the Newton and quasi-Newton methods are usually used due to their rapid convergence within the neighborhood of the solution set. The major drawbacks of these methods are operations with the Jacobian matrix at every iteration. Thus, researches have focused on spectral and conjugate gradient type methods due to their simplicity, minimum storage requirements, and better convergence properties which is important especially for solving large-scale problems. The authors propose a modified optimal Perry conjugate gradient method. An optimal choice for the scaled parameter is obtained by minimizing the difference between the largest and smallest eigenvalues of the search direction matrix. The method is incorporated with the hyperplane projection technique to exploit the advantages of the well-known predictor-corrector technique. The result is a robust algorithm for solving convex constrained monotone equations with applications in image and signal recovery. The global convergence of the proposed method is established using monotonicity and Lipschitz continuity assumptions. Numerical experiments are performed on convex constrained large-scale monotone equations and on applications in image and signal restoration problems. Comparisons of the results with other recent relevant methods show high efficiency of the proposed method.
scientific article; zbMATH DE number 7630343
scientific article