Abstract
A method for the localization, characterization and computation of the stationary points of a continuously differentiable real-valued function ofn variables is presented. It is based on the combinatorial topology concept of the degree of a mapping associated with an oriented polyhedron. The method consists of two principal steps: (i) localization (and computation if required) of a stationary point in ann-dimensional polyhedron; (ii) characterization of a stationary point as a minimum, maximum or saddle point. The method requires only the signs of gradient values to be correct and it can be successfully applied to problems with imprecise values.
Abstract
Предложен метод ноиска, классификации и вычисления стационарных точек непрерывно дифференцируемой вещественной функцииn переменных. Метод основан на заимствованном из комбинаторной топологии цонятии стецени отображения, связанного с ориентированным многогранником. Метод состоит из двух основных щагов: 1) локализация (и, если необходимо, вычисление) стационарной точки вn-мерном многограннике; 2) классификация стационарной точки как точки минимума, максимума или седловой точки. Применение метода требует знания только знаков градиентов, поэтому данный метод может успещно исцользоваться для рещения задач с погрещностями в условиях.
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© M. N. Vrahatis, E. C. Triantafyllon, 1996
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Vrahatis, M.N., Triantafyllou, E.C. Locating, characterizing and computing the stationary points of a function. Reliable Comput 2, 187–193 (1996). https://doi.org/10.1007/BF02425923
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DOI: https://doi.org/10.1007/BF02425923