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 |
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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 |
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