Tato diplomová práce se zabývá problematikou spojitého optimálního řízení, což je jedna z nejvýznamnějších aplikací teorie diferenciálních rovnic. Cílem této práce bylo jak nastudování matematické teorie optimálního řízení, tak především ukázat užití Pontrjaginova principu maxima a Bellmanova principu optimality při řešení vybraných úloh optimálního řízení. Důraz byl kladen především na problematiku časově a energeticky optimálního řízení elektrického vlaku, při zahrnutí kvadratické odporové funkce.

This thesis deals with the distributed and stochastic algorithms including testing their convergence in networks. The theoretical part briefly describes above mentioned algorithms, including their division, problems, advantages and disadvantages. Furthermore, two distributed algorithms and two stochastic algorithms are chosen. The practical part is done by comparing the speed of convergence on various network topologies in Matlab.

This thesis deals with the distributed and stochastic algorithms including testing their convergence in networks. The theoretical part briefly describes above mentioned algorithms, including their division, problems, advantages and disadvantages. Furthermore, two distributed algorithms and two stochastic algorithms are chosen. The practical part is done by comparing the speed of convergence on various network topologies in Matlab.

This thesis deals with the distributed and stochastic algorithms, including testing their convergence in networks. The theoretical part briefly describes above mentioned algorithms, including their division, problems, advantages and disadvantages. Futhermore, two distributed algorithms and two stochastic algorithms are chosen. The practical part is done by comparing the speed of convergence on various network topologies in MATLAB.

This thesis deals with shortest paths problem in graphs. Shortest paths problem is the basic issue of graph theory with many pracitcal applications. We can divide this problem into two following generalizations: single-source shortest path problem and all-pairs shortest paths problem. This text introduces principles and algorithms for generalizations. We describe both classical and new more efficient methods. It contains information about how some of these algorithms were implemented and offers an experimental comparison of these algorithms.