Abstract
In 1988, Barzilai and Borwein presented a new choice of step size for the gradient method for solving unconstrained minimization problems. Their method aimed to accelerate the convergence of the steepest descent method. The Barzilai-Borwein method has a low storage requirement and inexpensive computations. Therefore, many authors have paid attention to the Barzilai-Borwein method and have proposed some variants to solve large-scale unconstrained minimization problems. In this paper, we extend the Barzilai-Borwein-type methods of Friedlander et al. to more general class and establish global and Q-superlinear convergence properties of the proposed method for minimizing a strictly convex quadratic function. Furthermore, we apply our method to general objective functions. Finally, some numerical experiments are given.
| Original language | English |
|---|---|
| Pages (from-to) | 591-613 |
| Number of pages | 23 |
| Journal | Pacific Journal of Optimization |
| Volume | 6 |
| Issue number | 3 |
| Publication status | Published - 2010 Nov 9 |
| Externally published | Yes |
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Keywords
- Barzilai-Borwein method
- Global convergence
- Large-scale unconstrained minimization problem
- Q-superlinear convergence
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics
Cite this
Extended Barzilai-Borwein method for unconstrained minimization problems. / Narushima, Yasushi; Wakamatsu, Takahiko; Yabe, Hiroshi.
In: Pacific Journal of Optimization, Vol. 6, No. 3, 09.11.2010, p. 591-613.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Extended Barzilai-Borwein method for unconstrained minimization problems
AU - Narushima, Yasushi
AU - Wakamatsu, Takahiko
AU - Yabe, Hiroshi
PY - 2010/11/9
Y1 - 2010/11/9
N2 - In 1988, Barzilai and Borwein presented a new choice of step size for the gradient method for solving unconstrained minimization problems. Their method aimed to accelerate the convergence of the steepest descent method. The Barzilai-Borwein method has a low storage requirement and inexpensive computations. Therefore, many authors have paid attention to the Barzilai-Borwein method and have proposed some variants to solve large-scale unconstrained minimization problems. In this paper, we extend the Barzilai-Borwein-type methods of Friedlander et al. to more general class and establish global and Q-superlinear convergence properties of the proposed method for minimizing a strictly convex quadratic function. Furthermore, we apply our method to general objective functions. Finally, some numerical experiments are given.
AB - In 1988, Barzilai and Borwein presented a new choice of step size for the gradient method for solving unconstrained minimization problems. Their method aimed to accelerate the convergence of the steepest descent method. The Barzilai-Borwein method has a low storage requirement and inexpensive computations. Therefore, many authors have paid attention to the Barzilai-Borwein method and have proposed some variants to solve large-scale unconstrained minimization problems. In this paper, we extend the Barzilai-Borwein-type methods of Friedlander et al. to more general class and establish global and Q-superlinear convergence properties of the proposed method for minimizing a strictly convex quadratic function. Furthermore, we apply our method to general objective functions. Finally, some numerical experiments are given.
KW - Barzilai-Borwein method
KW - Global convergence
KW - Large-scale unconstrained minimization problem
KW - Q-superlinear convergence
UR - http://www.scopus.com/inward/record.url?scp=78049432839&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78049432839&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:78049432839
VL - 6
SP - 591
EP - 613
JO - Pacific Journal of Optimization
JF - Pacific Journal of Optimization
SN - 1348-9151
IS - 3
ER -