ON EFFECTIVE SEARCHING OF UNCONDITIONAL EXTREMUM SMOOTH FUNCTIONALS IN FINITE-DIMENSIONAL PROBLEMS
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Abstract
Conditions of fast convergence of simple iteration in a finite-dimensional task on an extremum for functionality of the third order of smoothness are received. Formulas of necessary number of operations for achievement of the set largest accuracy of coordinates of a stationary point and value of functionality are given in a stationary point. The differential iterative formula for a priori smooth functionalities, perhaps not representable in the form of composition of elementary functions is received. Equivalence of an order of accuracy of the received iterative formulas is shown, the upper bound of an optimum step is defined. Efficiency of a method of search of points of an extremum and points of the pass is shown in examples and computer programs.
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References
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