Mixed-Integer Nonlinear Optimization: Approaches and Applications (PRIN)


2014 to 2017
Mathematical Optimization (MO) applied to Decision Making is nowadays, together with other disciplines like statistics and simulation, an established methodology for pursuing efficiency, reliability and safety in a variety of contexts such as (to mention but a few) energy production and distribution, smart mobility, and green technology. This is testified at the European Union level by the kick-off of the COST Action TD1207 "Mathematical Optimization in the Decision Support Systems for Efficient and Robust Energy Networks", within the ICT domain, which aims at fostering the tight collaboration among energy experts, decision makers, engineers and mathematicians to improve efficiency, safety and reliability of energy production and distribution.
From a mathematical perspective, this success is due to the impressive progress within the last decades of two specific research areas, namely Discrete Optimization (DO) and Nonlinear Programming (NLP). Almost in isolation from each other, DO and NLP have been able to successfully link methodological advances with software development, a process fostered and stimulated by the goal of solving real-world applications. These remarkable achievements are demonstrated by the variety of high-quality open-source software tools currently available and, simultaneously, by a handful of commercial software tools that compete, by closer and closer releases, on the exciting software market of optimization.
The last kick that is allowing MO to establish itself so firmly as a reference tool for Decision Making has been the final merge of DO and NLP. Indeed, many real-world applications require to simultaneously deal with discrete decisions (one unit is on or off, etc.) and nonlinear characteristics of the (physical) systems (energy-to-fuel conversion, etc.) giving rise to problems that would be totally intractable without specific algorithmic techniques derived within this unified framework currently known as Mixed-Integer Non Linear Programming (MINLP).
This final merge is relatively recent, with significant milestones as the successful joint research program between Carnegie Mellon University and IBM T.J. Watson Research in 2005 in the USA, the PRIN2009 "Integrated Approaches for Discrete and Non Linear Optimization" in Italy and the Marie-Curie ITN "Mixed-Integer Nonlinear Optimization" FP7-PEOPLE-ITN-2012 at the EU level.
While the PRIN2009 project was still in the pioneering side of MINLP, trying to create solid connections between the two distinct communities and studying the links between the corresponding theoretical foundations, the current project aims at making a substantial step further, not only by integrating DO techniques within NLP and vice versa, but also by developing ad hoc algorithms and unified methodological frameworks. This will contribute to kick-starting the positive feedback loop between theoretical analysis and applications, with far-reaching consequences both on MO and on many applied fields.
Financed by: PRIN 2012 Ministero dell'Istruzione, dell'Università e della Ricerca