TY - JOUR
T1 - Memoryless quasi-newton methods based on spectral-scaling broyden family for unconstrained optimization
AU - Nakayama, Shummin
AU - Narushima, Yasushi
AU - Yabe, Hiroshi
N1 - Funding Information:
Acknowledgment. This research is supported in part by JSPS KAKENHI (grant number 17K00039). The authors are grateful to the anonymous referees whose comments helped to improve the paper.
Publisher Copyright:
© 2019 American Institute of Mathematical Sciences.
PY - 2019
Y1 - 2019
N2 - Memoryless quasi-Newton methods are studied for solving largescale unconstrained optimization problems. Recently, memoryless quasi-Newton methods based on several kinds of updating formulas were proposed. Since the methods closely related to the conjugate gradient method, the methods are promising. In this paper, we propose a memoryless quasi-Newton method based on the Broyden family with the spectral-scaling secant condition. We focus on the convex and preconvex classes of the Broyden family, and we show that the proposed method satisfies the sufficient descent condition and converges globally. Finally, some numerical experiments are given.
AB - Memoryless quasi-Newton methods are studied for solving largescale unconstrained optimization problems. Recently, memoryless quasi-Newton methods based on several kinds of updating formulas were proposed. Since the methods closely related to the conjugate gradient method, the methods are promising. In this paper, we propose a memoryless quasi-Newton method based on the Broyden family with the spectral-scaling secant condition. We focus on the convex and preconvex classes of the Broyden family, and we show that the proposed method satisfies the sufficient descent condition and converges globally. Finally, some numerical experiments are given.
KW - Broyden family
KW - Global convergence
KW - Memoryless quasi-Newton method
KW - Sufficient descent condition
KW - Unconstrained optimization
UR - http://www.scopus.com/inward/record.url?scp=85073284398&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85073284398&partnerID=8YFLogxK
U2 - 10.3934/jimo.2018122
DO - 10.3934/jimo.2018122
M3 - Article
AN - SCOPUS:85063199414
SN - 1547-5816
VL - 15
SP - 1773
EP - 1793
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 4
ER -