Využití proximal bundle metody pro nehladkou optimalizaci

Abstract

In practical applications we often have to solve the problem where the cost function is not differentiable. Thus we cannot directly use methods like Gradient Descent or Newton's methods. The aim of this thesis is to introduce method and implement an algorithm for nonsmooth optimization, namely the Proximal Bundle one. After briefly familiarization with a general optimization problem, we devote several chapters to nonsmooth analysis and optimization theory. The penultimate chapter consists of relatively detailed description of Proximal Bundle method algorithm and in the last part we summarize some numerical results obtained by our implementation in MATLAB.