The study of mathematical engineering focuses on developing mathematical disciplines used as theoretical foundations of engineering fields especially mechanical engineering. These are above all modern parts of approximate and numerical methods, stochastic methods, fuzzy and qualitative models, discrete mathematics, modern computer methods, parts of modern mathematical analysis. Doctoral dissertations are devoted both to developing the respective mathematical disciplines and to specific theoretical and experimental engineering problems.

prof. RNDr. Miloslav Druckmüller, CSc.

1. Advanced stochastic programming models

   Modern applied mathematical programs often involve uncertain parameters. Their presence significantly reduces usefulness of classical deterministic optimization techniques. So, stochastic programming belongs among the fundamental modelling approaches for decision making under risk and uncertainty. In model building phase, the important role is played by advanced deterministic reformulations and their transformations. The goal of the proposed research is to modify existing and develop original deterministic reformulations and to study their theoretical properties, solvability, applicability and connectivity.

   Tutor: Popela Pavel, RNDr., Ph.D.

2. Distributed and hierarchical mathematical programs

   Recent challenges in the solution of some advanced engineering optimization problems are related to their specialised hierarchical and distributed structure. Such a structure influences theoretical properties of models and also efficiency of classical approaches to modelling and solving. Thus, the important role is played by suitable modelling techniques, which further influence development of new and modification of existing algorithms. So, the proposed research task in the area of mathematical programming is to enhance existing and develop new hierarchical and distributed apporaches to modelling and solution of mathematical programs together with their implementation and application.

   Tutor: Popela Pavel, RNDr., Ph.D.