The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization |
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Authors: | Zengxin Wei Gaohang Yu Gonglin Yuan Zhigang Lian |
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Affiliation: | (1) Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, People's, Republic of China |
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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 Bk+1sk = y*k, where y*k is the sum of yk and Aksk, and Ak 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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Keywords: | unconstrained optimization quasi-Newton method superlinear convergence |
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