Mathematical Methods of Operations Research
start of the project: 2001 , end of the project: 30.09.2009
funding institution: German Academic Exchange Service (A/01/13017-212/ws)
principal investigatorProf. em. Dr. Frank Lempio
external project membersMatthias Gerdts (University of the Federal Armed Forces in Munich)
aims of the project
Mathematical methods of operations research serve as a tool for decision finding in technical and oeconomical application fields. Main topics are variants of the simplex algorithm, nonlinear programming, sensitivity analysis, dynamic optimization, network flow problems, network planning, integer and combinatorial optimization (branch, bound and cut-methods), fuzzy methods, neural networks, genetic algorithms.
Within this project, optimality conditions for continuous dynamic optimization problems are investigated under weak regularity assumptions on the optimal controls (key word: broken extremals). These conditions are relevant for stability analysis and for the foundation of discretization methods for the numerical solution of nonlinear control problems.
In parallel, a two semester curriculum of mathematical methods of operations research is developed which introduces the most important methods including mathematical modelling. This project was supported by a grant of a guest chair during WS 2001/02 and SS 2002 for Acad. Prof. Dr. P. Kenderov, Bulgarian Academy of Sciences, Sofia, within the international guest docent program INNOVATEC of the German Academic Exchange Service.
The essential contents of this curriculum were published as lecture script. In the moment a book on optimization methods in operations research is being prepared.
During the period 2005-2007, R. Baier and M. Gerdts were invited as lecturers of an intensive course on "Set-Valued Numerical Analysis and Optimal Control" in the year 2005 at Sofia and Borovets (Bulgaria) within the Center of Excellence for Applications of Mathematics (funded by DAAD).
Please go to the list of publications of this project.