Implementace bundle trust metody pro konvexní a nekonvexní úlohy nehladké optimalizace

Abstract

The thesis deals with methods for minimizing non-smooth functions, these are functions that are undifferentiable. The problem of minimization can be addressed indirectly by replacing functions by continuously differentiable approximation, or by algorithms that are suitable for minimizing non-differentiable functions. Between these methods belongs subgradient methods and bundle methods. In this work we will learn about one of the bundle methods - the bundle trust method, we will describe it in detail, implement it and try it on selected functions. We will introduce the basic theory of non-smooth optimalization before focusing on the bundle trust method.