An active-set memoryless quasi-Newton method based on a spectral-scaling Broyden family for bound constrained optimization

Shummin Nakayama; Yasushi Narushima; Hiroaki Nishio; Hiroshi Yabe

doi:10.1016/j.rico.2021.100012

An active-set memoryless quasi-Newton method based on a spectral-scaling Broyden family for bound constrained optimization

Shummin Nakayama, Yasushi Narushima, Hiroaki Nishio, Hiroshi Yabe

Department of Industrial and Systems Engineering

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we consider an active-set algorithm for solving large-scale bound constrained optimization problems. First, by incorporating a restart technique, we modify the active-set strategy by Yuan and Lu (2011) and combine it with the memoryless quasi-Newton method based on a modified spectral-scaling Broyden family. Then, we propose an algorithm of our method with the framework of the Armijo line search, and show its global convergence. Finally, we illustrate some numerical experiments to investigate how the parameter choice in our method affects numerical performance.

Original language	English
Article number	100012
Journal	Results in Control and Optimization
Volume	3
DOIs	https://doi.org/10.1016/j.rico.2021.100012
Publication status	Published - 2021 Jun

Keywords

Active-set method
Bound constrained optimization
Broyden family
Global convergence
Memoryless quasi-Newton method

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics
Artificial Intelligence
Modelling and Simulation
Control and Systems Engineering

Access to Document

10.1016/j.rico.2021.100012

Cite this

@article{e444149a83484402a089734a3d40f77b,

title = "An active-set memoryless quasi-Newton method based on a spectral-scaling Broyden family for bound constrained optimization",

abstract = "In this paper, we consider an active-set algorithm for solving large-scale bound constrained optimization problems. First, by incorporating a restart technique, we modify the active-set strategy by Yuan and Lu (2011) and combine it with the memoryless quasi-Newton method based on a modified spectral-scaling Broyden family. Then, we propose an algorithm of our method with the framework of the Armijo line search, and show its global convergence. Finally, we illustrate some numerical experiments to investigate how the parameter choice in our method affects numerical performance.",

keywords = "Active-set method, Bound constrained optimization, Broyden family, Global convergence, Memoryless quasi-Newton method",

author = "Shummin Nakayama and Yasushi Narushima and Hiroaki Nishio and Hiroshi Yabe",

note = "Funding Information: This research was supported in part by JSPS, Japan KAKENHI (grant number 18K11179 and 20K11698) and the Research Institute for Mathematical Sciences in Kyoto University, Japan . The authors are grateful to the anonymous referees whose comments helped to improve the paper. Publisher Copyright: {\textcopyright} 2021 The Author(s)",

year = "2021",

month = jun,

doi = "10.1016/j.rico.2021.100012",

language = "English",

volume = "3",

journal = "Results in Control and Optimization",

issn = "2666-7207",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - An active-set memoryless quasi-Newton method based on a spectral-scaling Broyden family for bound constrained optimization

AU - Nakayama, Shummin

AU - Narushima, Yasushi

AU - Nishio, Hiroaki

AU - Yabe, Hiroshi

N1 - Funding Information: This research was supported in part by JSPS, Japan KAKENHI (grant number 18K11179 and 20K11698) and the Research Institute for Mathematical Sciences in Kyoto University, Japan . The authors are grateful to the anonymous referees whose comments helped to improve the paper. Publisher Copyright: © 2021 The Author(s)

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, we consider an active-set algorithm for solving large-scale bound constrained optimization problems. First, by incorporating a restart technique, we modify the active-set strategy by Yuan and Lu (2011) and combine it with the memoryless quasi-Newton method based on a modified spectral-scaling Broyden family. Then, we propose an algorithm of our method with the framework of the Armijo line search, and show its global convergence. Finally, we illustrate some numerical experiments to investigate how the parameter choice in our method affects numerical performance.

AB - In this paper, we consider an active-set algorithm for solving large-scale bound constrained optimization problems. First, by incorporating a restart technique, we modify the active-set strategy by Yuan and Lu (2011) and combine it with the memoryless quasi-Newton method based on a modified spectral-scaling Broyden family. Then, we propose an algorithm of our method with the framework of the Armijo line search, and show its global convergence. Finally, we illustrate some numerical experiments to investigate how the parameter choice in our method affects numerical performance.

KW - Active-set method

KW - Bound constrained optimization

KW - Broyden family

KW - Global convergence

KW - Memoryless quasi-Newton method

UR - http://www.scopus.com/inward/record.url?scp=85115996305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85115996305&partnerID=8YFLogxK

U2 - 10.1016/j.rico.2021.100012

DO - 10.1016/j.rico.2021.100012

M3 - Article

AN - SCOPUS:85115996305

SN - 2666-7207

VL - 3

JO - Results in Control and Optimization

JF - Results in Control and Optimization

M1 - 100012

ER -

An active-set memoryless quasi-Newton method based on a spectral-scaling Broyden family for bound constrained optimization

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this