A descent improved three-term derivative-free spectral gradient projection approach for solving monotone nonlinear equations with convex constraints

Abstract

In this paper, based on projection technique Solodove and Svaiter (Reformulation: Nonsmooth, piecewise smooth, semismooth and smoothing methods; 355-369,1995 ), we propose a decent improved three-term derivative free approach for solving nonlinear monotone equations with convex constraints. The algorithm combines the spectral gradient parameter with a newly PRPlike CG coefficient in the search direction. The global convergence of the proposed approach established under standard conditions. Additionally, using some benchmark problems, the numerical results highlight the outstanding performance of this approach compared to popular conjugate gradient methods. The experiments also show its effectiveness in solving large-scale nonlinear equations with convex constraints.