Decomposition Techniques for Large-Scale Energy Optimization Problems

The current Ph.D. Thesis has as its main focus and research area the field of Combinatorial Optimization. The aim is to further develop and improve some of the techniques and methods that are used to solve hard Combinatorial Optimization problems, among which are algorithmic Convex Analysis, Mixed Integer Linear Programming and Decomposition Approaches. We are interested in both exploring (and further enriching) the theoretical understanding of these fields, and also in creating efficient algorithmic tools in order to apply these methods in the most effective way. Hence, in the thesis we will try to properly balance the theoretical investigation with actual implementation of the proposed approaches and their testing on real-world optimization problems, in particular related to electrical energy production and distribution.