TY - JOUR
T1 - Extra updates for the BFGS method
AU - Al-Baali, M.
N1 - Funding Information:
This research was supported in part by the Italian Ministry of University Grant. Some of the work was done during the author's visit to Calabria University. The author is grateful to Lucio Grandinetti for his arrangement of the visit and to the staff members of the Department of Electronics,
PY - 2000
Y1 - 2000
N2 - This paper considers employing extra updates for the BFGS method for unconstrained optimization. The usual BFGS Hessian is updated a number of times, depending on the information of the first order derivatives, to obtain a new Hessian approximation at each iteration. Two approaches are proposed. One of them has the same properties of global and superlinear convergence on convex functions the BFGS method has, and another has the same property of quadratic termination without exact line searches that the symmetric rank-one method has. The new algorithms attempt to combine the best features of certain methods which are intended for either parallel computation or large scale optimization. It is concluded that some new algorithms are competitive with the standard BFGS method.
AB - This paper considers employing extra updates for the BFGS method for unconstrained optimization. The usual BFGS Hessian is updated a number of times, depending on the information of the first order derivatives, to obtain a new Hessian approximation at each iteration. Two approaches are proposed. One of them has the same properties of global and superlinear convergence on convex functions the BFGS method has, and another has the same property of quadratic termination without exact line searches that the symmetric rank-one method has. The new algorithms attempt to combine the best features of certain methods which are intended for either parallel computation or large scale optimization. It is concluded that some new algorithms are competitive with the standard BFGS method.
UR - http://www.scopus.com/inward/record.url?scp=0033658985&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033658985&partnerID=8YFLogxK
U2 - 10.1080/10556780008805781
DO - 10.1080/10556780008805781
M3 - Article
AN - SCOPUS:0033658985
SN - 1055-6788
VL - 13
SP - 159
EP - 179
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 3
ER -