A new filled function for nonsmooth global optimization

Abstract

In this paper we offer a new filled function for finding global minimizer of a nonsmooth function on a closed bounded set. Unlike any traditional filled function the proposed filled function can be used for uniformly continuous functions. We also test this new filled function on uniformly continuous but not necessarily Lipschitz continuous test functions.

Non-smooth modeling in surface hardening

“…In this work, we try to model the effect of the amount of alloying elements which are amount of carbon (C) and silicon (Si) on microhardness. Finally, local and global extremum values of the objective function are obtained by applying filled function method which is one of the effective global optimization techniques, that has recently been started to be applied to these kinds of physical problems (see [29][30][31]).…”

“…Just replacing x * 1 by x * 2 , a new filled function can be constructed and then a much lower minimizer of the objective function can be found by using the same way. This loop continues until the global minimizer of the objective function is found [29][30][31][32][33].…”