The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization.

The BEGS 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+1s_k = y_k^*, where y_k^* is the sum of y_k and A_ks_k, and A_k is some matrix, The average performance of Algorithm 4.3 in [16] is better than that of the BEGS method, but its superlinear convergence is still open. This article proves the superlinear convergence of Algorithm 4.3 under some suitable conditions. [ABSTRACT FROM AUTHOR]