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

Abstract

In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai-{L}iao condition and the descent three-term CG search direction. Both parameters are incorporated with the projection technique for solving large-scale monotone nonlinear equations. Using the Lipschitz and monotone assumptions, the global convergence of methods has been proved. Finally, numerical results are provided to illustrate the robustness of the proposed methods.

A New Hybrid Conjugate Gradient Projection Method for Solving Nonlinear Monotone Equations

“…Tese are derivative-free methods, where JKL and EMDY methods are the state-of-the-art methods. Among them, the JKL method, PDY method, and HG method use the line search of formula (17), and the EMDY method uses the line search of formula (18). All codes used were written in Matlab R2015a and run on PC with 4 GB of RAM and Windows 10 operating system.…”

“…Yin et al [16] proposed a hybrid three-term conjugate gradient projection method, whose search direction is close to the search direction generated by the memoryless BFGS method and possesses a descending characteristic independent of the line search technique as well as a trust region characteristic. Using the adaptive line search technique, the global convergence of the method is established under certain mild conditions, and numerical experiments demonstrate that the method inherits the benefcial properties of the three-term conjugate gradient method and the hybrid conjugate gradient method [17,18]. Zhou et al [19] proposed a novel hybrid PRPFR conjugate gradient method with sufcient descent and trust region properties.…”

A new three-term conjugate gradient method for solving the finite minimax problems

“…There are many well-known conjugate gradient methods, such as [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][34][35][36][37][38][39][40][41][42]. In [12], the iterative formula of three-term conjugate gradient method is…”

“…For three-term conjugate gradient methods [12][13][14][15][16][17][18][19][20][21][22] and the related methods [23][24][25][26] posse low memory requirement and simple implementation, conjugate gradient methods are often used for solving unconstrained optimization problems. Recently, many researchers have presented kinds of three-term conjugate gradient method for solving the unconstrained optimization problems.Hence, we consider using three-term conjugate gradient method to solve the finite minimax problems.…”

A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

“…The spectral gradient (SG) and conjugate gradient (CG) methods are another set of methods, which are used to solve systems of nonlinear equations. These methods are matrix-free; they can successfully handle largescale problems, see [8][9][10][11][12][13][14][15] and the references therein. The main iterative procedure of CG methods for the system of monotone equations given an initial point x 0 is…”