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Abstract

Complex decision-making in enterprises should involve mathematical optimization methods, because a “best choice” has to be made out of a huge number of feasible options. A mathematical description of such decision processes typically involves both “continuous” and “discrete” decisions. If the latter are present, the customary modeling approach is to use integer variables, which are also used to represent all possible nonlinearities, so that the remaining part of the model is linear. This leads to Mixed-Integer Linear Optimization (MILO) problems, which can be handled nowadays by many packages, but are often very difficult to solve.

The difficulty of MILO problems is often due to the fact that objective functions or constraints that are structurally nonlinear (e.g., quadratic) are linearized by introducing new integer variables. In many cases, it was observed that this is not the best way to proceed, as facing the nonlinearity directly without the new variables leads to much better results. Algorithmic technology for the resulting Mixed-Integer Nonlinear Optimization (MINO) problems is still at its early stage.

The present situation is that enterprises facing a MINO problem generally give up due to the lack of efficient solvers, or try to convert it to a MILO one often too hard to be solved in practice. On the other hand, in the academia there is now an increasing expertise in MINO, which is however hardly exported outside due to the lack of interaction with the industrial world. It is the purpose of this project to help satisfy the increasing demand for highly qualified researchers receiving, at the same time, a state-of-the-art scientific training from the academia and hands-on experience with real-world applications from the industry.

The researchers formed within this project, once recruited by an enterprise at the end of their training, will have the potential to apply all the available knowledge to optimize complex decision-making in the real world.