Introduction to Decomposition Techniques in Mathematical Programming: Modelling, Algorithms, Examples, Applications and Visualization
seminar organised by the Department of Statistics & OR
speaker: Prof. Pavel Popela
date: Friday 10 May
time: 12:00 noon
venue: Room 602, Maths & Physics Building (MP602)
venue: Room 602, Maths & Physics Building (MP602)
Abstract
The actual real-world decision making problems are often modeled by complex mathematical programs that involve uncertain parameters, continuous and discrete variables, nonlinear terms and time related decision stages.
Frequently, they can be approximated by large-scale linear (or nonlinear) models having a special structure that may allow the use of special purpose, so called decomposition, algorithms. Hence, the main purpose of the talk is to introduce some key ideas behind these techniques. At first, it will be shown how Ideas of penalty terms and a cutting plane algorithm lead to so called Benders decomposition. Then, aggregated models involving scenario related data are discussed. Alternatively, they can be relaxed and convergence of sequences of parallel solutions can be obtained again by another use of penalty ideas. The presentation can be interesting for both groups of university teachers and students of all years of study as theoretical principles and description of algorithms will be accompanied by explanatory examples with visualization of computations. It is important to emphasize that decomposition techniques still represent interesting field for actual research and for future diploma thesis.
At the end, several applications and generalizations will be mentioned.