Implementace gradient sampling metody pro úlohy nehladké optimalizace

Abstract

This bachelor’s thesis addresses the issue of nonsmooth optimization, with a primary focus on the Gradient Sampling method and its implementation. The main objective is to describe the basic concepts, which primarily include Clarke’s subdifferential. Furthermore, the thesis describes the principle of the Gradient Sampling method itself, which uses gradient sampling in the vicinity of the current point to approximate the generalized gradient and subsequently determine the descent direction, as well as its specific implementation in Python, which is supplemented by a real-world application. The method is tested on a selected set of test problems, the results of which demonstrate the method’s ability to effectively find the minimum of a non-smooth function, although its behavior depends on the choice of initial parameters.