A modified scaling parameter for the memoryless BFGS updating formula

Based on an eigenvalue analysis, condition number of the scaled memoryless BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula is obtained. Then, a modified scaling parameter is proposed for the mentioned updating formula, minimizing the given condition number. The suggested scaling parameter can be considered as a modified version of the self–scaling parameter proposed by Oren and Spedicato. Numerical experiments are done; they demonstrate practical effectiveness of the proposed scaling parameter.

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