A descent derivative-free algorithm for nonlinear monotone equations with convex constraints

¹ Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, 700241 Kano, Nigeria
² Fixed Point Research Laboratory, Department of Mathematics, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 10140 Thrung Khru, Bangkok, Thailand

^* Corresponding author: hmuhd.mth@buk.edu.ng

Received: 1 April 2019
Accepted: 27 January 2020

Abstract

In this paper, we present a derivative-free algorithm for nonlinear monotone equations with convex constraints. The search direction is a product of a positive parameter and the negation of a residual vector. At each iteration step, the algorithm generates a descent direction independent from the line search used. Under appropriate assumptions, the global convergence of the algorithm is given. Numerical experiments show the algorithm has advantages over the recently proposed algorithms by Gao and He (Calcolo 55 (2018) 53) and Liu and Li (Comput. Math. App. 70 (2015) 2442–2453).