Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations

Abstract

In this paper, we propose a self adaptive spectral conjugate gradient-based projection method for systems of nonlinear monotone equations. Based on its modest memory requirement and its efficiency, the method is suitable for solving large-scale equations. We show that the method satisfies the descent condition F T k d k ≤ −c F k 2 , c > 0, and also prove its global convergence. The method is compared to other existing methods on a set of benchmark test problems and results show that the method is very efficient and therefore promising.

An efficient three-term conjugate gradient-type algorithm for monotone nonlinear equations

“…This section provide the numerical tests using the proposed Algorithm 2.1. The algorithm is coded in Matlab and comparison is provided in term efficiency with the NHZ derivative-free method [7] and the Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations (SASCG) [19]. However, for the proposed algorithms we selected τ = 1, γ = 0.9, δ = 0.0001 and ξ 0 = 0.06.…”

“…• Tables 1-4 showed the numerical efficiency of the proposed methods compared to the NHZ method [7] and the SASCG method [19]. In our comparison, ITER is set to represent the number of iterations, TIME for the CPU time in the second, FVL for the number of function evaluations, and NORM to indicate the norm of the function evaluation at the stopping point.…”

“…On the following initial guesses, we considered eight test problems, namely, Table 1. Numerical performance of the Algorithm 2.1 with the choices of β 1 k , β 2 k , NHZ method [7] and SASCG method [19]. Table 2.…”

“…Numerical performance of the Algorithm 2.1 with the choices of β 1 k , β 2 k , NHZ method [7] and SASCG method [19]. [7] and SASCG method [19] (with respect to number of iteration). [7] and SASCG method [19] (with respect to CPU time).…”

Show off the efficiency of dai-liao method in merging technology for monotonous non-linear problems

“…Likewise, when these methods overlap with the projection technique proposed by Solodov and Svaiter [13] to solve large-scale nonlinear equations and constrained nonlinear equations that some researchers have expanded as in [14][15][16][17][18][19]. Recently, many researchers have presented articles on how to find the solution to both constrained and unconstrained monotones (1) and give them a lot of attention [20][21][22][23][24][25][26][27]. Include the idea of projection that needs to be accelerated using a monotonous case F by monotony F and letting , the hyperplane: Separates strictly from the solution set of (2).…”