A Robust Spectral Three-Term Conjugate Gradient Algorithm for Solving Unconstrained Minimization Problems

Abbas Al-Bayati,Sabreen Abbas

doi:10.33899/csmj.2020.163504

Abstract

In this paper, we investigated a new improved Conjugate Gradient (CG) algorithm of a Three-Term type (TTCG) based on Dai and Liao procedure to improve the CG algorithm of (Hamoda, Rivaie, and Mamat / HRM). The new CG-algorithm satisfies both the conjugacy condition and the sufficient descent condition. The step-size of this TTCG-algorithm would be computed by accelerating the Wolfe-Powell line search technique. The proposed new TTCG algorithms have demonstrated their global affinity in certain specific circumstances given in this paper.

Highlights

To start by giving any issue of unconstrained optimization we need to know this issue as follows: min {f(x): x ∈ Rn} (1)Let us define the function as f from Rn to R is continuously differentiable function, Abbas Y
Abbas and its gradient is denoted by g(x) = ∇f(x), these Conjugate Gradient (CG) methods are known to be designed to solve the problem of type (1), when the n dimension is very large due to the simplicity of repetition of the search, memory requirements are very low
This paper is divided as follows: In Section 2, we evaluate the new form of the CG-three-term method using the spectral gradient method with derivation of θkSBi, i = 1,2,3

Summary

. Introduction

To start by giving any issue of unconstrained optimization we need to know this issue as follows: min {f(x): x ∈ Rn}. From the results that obtained by [15], the quantity of the parameter u=0.9 i.e. u ∈ (0,1) and from βkHRM given in equation (8), the search direction of this formula was given in the following gradient:. In 1988, Raydan [19] added SCG method to the problems of unrestricted improvement on a large scale The idea of this method depends mainly on the use of gradient trends only in each line search in order to ensure the regression strategy by multiplying the first limit by a parameter derived from one of the known derivation methods or by the parameter βk as in the first idea of this method, Good global. Liu et al [10] make an adjustment to the CD-method so that the direction that is always generated is the descent direction and dk is determined by the following:

CD k

Test Problems

No of NEW

Conclusions