Вычислительные методы и приложения

Computing quasi-differentials and exhausters by function values

M. Yu. Andramonov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: A general method for computing quasi-differentials and co-differentials is proposed; the method is based on their approximation by polygons. The accuracy of approximation depends on the numbers of vectors for which the directional derivative is computed. The algorithm can be used for nonsmooth optimization, in particular, in Newton's method and the steepest descent method for minimizing complicated non-differentiable functions.

Keywords: numerical methods of optimization, nonsmooth optimization, quasi-differentials, gradient methods, exhausters.