Abstract
The BFGS method is the most effective of the quasi-Newton methods for solving unconstrained optimization problems. Wei, Li, and Qi [16] have proposed some modified BFGS methods based on the new quasi-Newton equation B k+1 s k = y* k , where y* k is the sum of y k and A k s k, and A k is some matrix. The average performance of Algorithm 4.3 in [16] is better than that of the BFGS method, but its superlinear convergence is still open. This article proves the superlinear convergence of Algorithm 4.3 under some suitable conditions.
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Wei, Z., Yu, G., Yuan, G. et al. The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization. Computational Optimization and Applications 29, 315–332 (2004). https://doi.org/10.1023/B:COAP.0000044184.25410.39
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DOI: https://doi.org/10.1023/B:COAP.0000044184.25410.39