TY - JOUR
T1 - A steepest descent method with a Wolf type line search
AU - Ju Jing-jie and Pang De-yan and Du Shou-qiang
JO - Journal of Information and Computing Science
VL - 4
SP - 252
EP - 261
PY - 2024
DA - 2024/01
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22568.html
KW - the steepest decent method, line search, global convergence 

AB -  The  steepest  decent  method  is  proposed  by French  mathematician  Cauchy  and  it  is one  of  the 
simplest and oldest methods for solving unconstrained optimization problems. The steepest descent method, 
negative gradient direction is chosen as the search direction, also known as the gradient method. Usually, the 
step length α(cid:2921) of the steepest decent method can be computed by some inexact line search. In this paper, we 
will use a Wolfe type line search to evaluate the step length and its convergence property will be given under 
mild assumptions. From the numerical results, we can see that the steepest descent method with this Wolfe 
type  line  search  is  very  promising.  Finally,  we  give  an  application  of  the  method  to  solve  the  nonlinear 
complementarity problem.