A Global Convergence of Spectral Conjugate Gradient Method for Large Scale Optimization

Ghada M Al-Naemi

doi:10.33899/edusj.2018.159323

Abstract

A Global Convergence of Spectral Conjugate Gradient Method for Large Scale Optimization

Highlights

Let f : Rn → R be continuously differentiable function
A conjugate gradient (CG) method generates a sequence of iterates by letting xk = xk −1 + k −1dk −1, k=0,1,2
In this paper we proposed two spectral CG method, they based to the modification to the standard conjugate descent (CD) in (4), and proposed a suitable k for each one to get a good spectral CD-CG methods

Summary

Introduction

Let f : Rn → R be continuously differentiable function. Consider the unconstrained nonlinear optimization problem: Minimize f(x), x Rn. We use g(x) to denote to the gradient of f at x. Due to need less computer memory especially, conjugate gradient method is very appealing for solving (1) when the number of variables is large. A conjugate gradient (CG) method generates a sequence of iterates by letting xk = xk −1 + k −1dk −1, k=0,1,2,. Where k is scalar which determines the different CG methods [11]. In survey paper Hager and Zhang in [9] reviewed the development of different various of nonlinear gradient methods, with especial attention given to global convergence properties

CD k by

FR formula and d

We are going to prove that

MCD k

NOF NOI