Spectral Scaling BFGS Method

W. Y. Cheng () and D. H. Li ()
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W. Y. Cheng: Dongguan University of Technology
D. H. Li: South China Normal University

Journal of Optimization Theory and Applications, 2010, vol. 146, issue 2, No 4, 305-319

Abstract: Abstract In this paper, we scale the quasiNewton equation and propose a spectral scaling BFGS method. The method has a good selfcorrecting property and can improve the behavior of the BFGS method. Compared with the standard BFGS method, the single-step convergence rate of the spectral scaling BFGS method will not be inferior to that of the steepest descent method when minimizing an n-dimensional quadratic function. In addition, when the method with exact line search is applied to minimize an n-dimensional strictly convex function, it terminates within n steps. Under appropriate conditions, we show that the spectral scaling BFGS method with Wolfe line search is globally and R-linear convergent for uniformly convex optimization problems. The reported numerical results show that the spectral scaling BFGS method outperforms the standard BFGS method.

Keywords: Unconstrained optimization; BFGS method; Global convergence (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-010-9652-y

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