SEARCH FOR AN EXTREMUM USING THE STEEPEST DESCENT METHOD UNDER THE CONDITIONS OF EXPERIMENTAL ERRORS
Abstract
One of the spread first level methods of optimum search is learned by the steepest descent method in conditions when there are mistakes in the experiment. The steepest descent method is investigated and is successfully applied in situations, when, there are no mistakes of experiment. However, in real situations the used means of measurement always have determined errors owing to what the appropriate meanings of the response receives with mistakes. The model of the steepest descent algorithm in created, when the length of the step does not depend on the meaning of the purpose functioning. Stepping process realization algorithm and program provision in MathCAD, computer mathematic, system is designed. The realization outcome mistakes for different meaning are presented, the step movement of the optimum dot direction is shown according to function meaning and argument meaning as well. The amount needed for the tactics necessary to approach the minimum is established, the quake amplitude in the surrounding of different level experiment mistakes at the optimum search efficiency in different step conditions.
References
Éric Walter, Numerical Methods and Optimization, Springer, Cham, Number of PagesXV, 476, Springer International Publishing Switzerland 2014.
Otkhozoria n, Zedhinidze I. Extreme search by simplex method under experimental error conditions Scientific-Periodical Journal "Intellect", N2, (16), 2003.
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