VARIABLE METRIC METHODS WITH OPTIMUM DIFFERENCE APPROXIMATIONS OF DERIVATIVES
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Abstract:
On the basis of the relation between truncation and rounding errors of difference approximation, the interval formula which can minimize the total error is founded. The method choosing optimum interval is applied to unconstrained VMM(Variable Metric Method), SUMT-DFP, and constrained VMM. Three optimization methods with optimum difference approximations are presented. These methods are very efficient, especially when dealing with complex problem functions.
