A spectral conjugate gradient method for convex constrained monotone equations

Shi Lei

ABSTRACT: Based on the projection technique, in this paper we establish a spectral conjugate gradient method to solve nonlinear monotone equations with convex constraints. A nice property is that its search direction always satisfies the sufficient descent condition in each iteration, which is independent of any line search. Because there is not any derivative information, the proposed method is very suitable to solve large-scale nonsmooth monotone equations. By using a derivative-free line search, the global convergence is proved under the Lipschitz continuity. Preliminary numerical experiments show that the proposed method is effective and promising.

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^a	General Education and International College, Chongqing College of Electronic Engineering, Chongqing 5401331 China

* Corresponding author, E-mail: shileimath@163.com

Received 9 Jan 2021, Accepted 5 May 2021