Abstract
Undesirable effects of the direction of the maximum magnification by the scaled memoryless BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula are studied, including some probable computational errors as well as weakening the convergence. In light of the insight gained by our analyses, a restart criterion for the method is suggested to accelerate convergence and also to decrease the errors. Convergence analysis of the given method is carried out as well. At last, the efficiency of the proposed restart approach is investigated by numerical tests on a set of CUTEr problems.
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