A Family of Derivative-Free Conjugate Gradient Methods for Constrained Nonlinear Equations and Image Restoration

IEEE Access

Wiyada Kumam¹  Abdulkarim Hassan Ibrahim¹  Poom Kumam² 

[1] Department of Mathematics, Faculty of Science, KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut&x2019;s University of Technology Thonburi (KMUTT), Bangkok, Thailand;

关键词: Unconstrained optimization;    nonlinear equations;    convex constrained;    conjugate gradient method;    projection method;    compressive sensing;   

DOI  :  10.1109/ACCESS.2020.3020969

来源: DOAJ

【 摘 要 】

In this paper, a derivative-free conjugate gradient method for solving nonlinear equations with convex constraints is proposed. The proposed method can be viewed as an extension of the three-term modified Polak-Ribiére-Polyak method (TTPRP) and the three-term Hestenes-Stiefel conjugate gradient method (TTHS) using the projection technique of Solodov and Svaiter [Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, 1998, 355-369]. The proposed method adopts the adaptive line search scheme proposed by Ou and Li [Journal of Applied Mathematics and Computing 56.1-2 (2018): 195-216] which reduces the computational cost of the method. Under the assumption that the underlying operator is Lipschitz continuous and satisfies a weaker condition of monotonicity, the global convergence of the proposed method is established. Furthermore, the proposed method is extended to solve image restoration problem arising in compressive sensing. Numerical results are presented to demonstrate the effectiveness of the proposed method.

【 授权许可】

Unknown