TY - JOUR
T1 - Damped Techniques for the Limited Memory BFGS Method for Large-Scale Optimization
AU - Al-Baali, Mehiddin
AU - Grandinetti, Lucio
AU - Pisacane, Ornella
N1 - Publisher Copyright:
© 2013, Springer Science+Business Media New York.
PY - 2014/5/1
Y1 - 2014/5/1
N2 - This paper is aimed to extend a certain damped technique, suitable for the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, to the limited memory BFGS method in the case of the large-scale unconstrained optimization. It is shown that the proposed technique maintains the global convergence property on uniformly convex functions for the limited memory BFGS method. Some numerical results are described to illustrate the important role of the damped technique. Since this technique enforces safely the positive definiteness property of the BFGS update for any value of the steplength, we also consider only the first Wolfe–Powell condition on the steplength. Then, as for the backtracking framework, only one gradient evaluation is performed on each iteration. It is reported that the proposed damped methods work much better than the limited memory BFGS method in several cases.
AB - This paper is aimed to extend a certain damped technique, suitable for the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, to the limited memory BFGS method in the case of the large-scale unconstrained optimization. It is shown that the proposed technique maintains the global convergence property on uniformly convex functions for the limited memory BFGS method. Some numerical results are described to illustrate the important role of the damped technique. Since this technique enforces safely the positive definiteness property of the BFGS update for any value of the steplength, we also consider only the first Wolfe–Powell condition on the steplength. Then, as for the backtracking framework, only one gradient evaluation is performed on each iteration. It is reported that the proposed damped methods work much better than the limited memory BFGS method in several cases.
KW - Damped technique
KW - Large-scale optimization
KW - Line search framework
KW - The limited memory BFGS method
UR - http://www.scopus.com/inward/record.url?scp=84944653600&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84944653600&partnerID=8YFLogxK
U2 - 10.1007/s10957-013-0448-8
DO - 10.1007/s10957-013-0448-8
M3 - Article
AN - SCOPUS:84944653600
SN - 0022-3239
VL - 161
SP - 688
EP - 699
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -