Modern Techniques in Discrete Optimization: Mathematics, Algorithms and Applications (15w5006)
The importance of this workshop is justified by the many computational advances that came as a result of deep mathematical methods and new interesting applications arising today. Exciting developments in the last seven years include the use of Fourier analysis to solve integer programs, the application of rational generating functions in multi-criteria problems, the use of representation theory to deal with semidefinite programs with underlying symmetry, and many more. In the application domain, the theme of data mining and information retrieval from partial data has become rather hot (e.g., Netflix matrix problem).
We will bring together researchers interested in the mathematical foundations of discrete optimization to discuss new tools and explore new techniques, in particularly regarding the use of algebraic, analytical, and geometric techniques to solve difficult optimization problems. This will be the first workshop bringing together researchers with this focus in North-America.
We aim to enhance the study of discrete optimization problems which include non-linear constraints. This topic has become a central theme in the last three years. Integer programmers have now turned their attention to solving problems with non-linear constraints and integer variables. Obviously non-linear integer models have much more expressive power and capture real phenomena better, but new techniques are required for finding solutions. Of course, for such models, complexity theory tells us that the such classes of models can even be undecidable, so the challenge is to find the right balance between expressiveness and tractability. We believe that advanced mathematical techniques can lead us to more expressive models that can be effectively solved (as compared to the current state-of-the-art).