A new gradient method via quasi-Cauchy relation which guarantees descent

Authors:
Malik Abu Hassan;Wah June Leong;Mahboubeh Farid
Affiliations:
Institue for Mathematical Research, University Putra Malaysia, 43300 Serdang, Selangor, Malaysia;Institue for Mathematical Research, University Putra Malaysia, 43300 Serdang, Selangor, Malaysia;Institue for Mathematical Research, University Putra Malaysia, 43300 Serdang, Selangor, Malaysia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 2
Cited 3

Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization

Computational Optimization and Applications
On the asymptotic behaviour of some new gradient methods

Mathematical Programming: Series A and B

A new two-step gradient-type method for large-scale unconstrained optimization

Computers & Mathematics with Applications
An improved multi-step gradient-type method for large scale optimization

Computers & Mathematics with Applications
A matrix-free quasi-Newton method for solving large-scale nonlinear systems

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

We propose a new monotone algorithm for unconstrained optimization in the frame of Barzilai and Borwein (BB) method and analyze the convergence properties of this new descent method. Motivated by the fact that BB method does not guarantee descent in the objective function at each iteration, but performs better than the steepest descent method, we therefore attempt to find stepsize formula which enables us to approximate the Hessian based on the Quasi-Cauchy equation and possess monotone property in each iteration. Practical insights on the effectiveness of the proposed techniques are given by a numerical comparison with the BB method.