Monique Laurent
Professor of Combinatorial Optimization at the Department of Econometrics and Operations Research and researcher at CWI. Monique is member of the Royal Netherlands Academy of Arts and Sciences (KNAW). Together with Professor Etienne de Klerk she received a Marie Sklodowska-Curie Innovative Training Networks consortium grant for their project “Polynomial Optimization, Efficiency through Moments and Algebra (POEMA)”.
Optimization is present everywhere: most processes in our daily lives involve some form of optimization.
What is the main goal of your research?
My research field is discrete mathematics and optimization. I am in particular interested in combinatorial optimization and, more generally, in polynomial optimization, where the objective function to be optimized and the constraints may involve polynomial nonlinearities. These are used to model problems in diverse application areas, such as logistics, energy, and quantum information. The goal of my research is to develop mathematical tools and efficient algorithms for such optimization problems. For this I try to understand and exploit geometric, combinatorial and algebraic structures and to combine tools from various mathematical areas aiming to obtain improved solution methods.
How does your research contribute to solving societal problems?
My own work is more on the fundamental side, but occasionally I also work on more applied projects. For instance I have collaborated with the BNG bank on an optimization algorithm for optimal hedging and I developed recently new combinatorial search algorithms which I hope may find applications for data ranking. In any case it is fair to say that optimization is present everywhere: most processes in our daily lives involve some form of optimization. As a very simple example, when searching your route on a navigation system, shortest path problems have to be solved!
I am happy to be part of a very nice community which can provide useful contributions to societal challenges. Of course I also expect that most of the more fundamental results of today will find later their ways into practical applications.
What is your main motivation?
Building bridges between areas, exploring new connections, gaining a more fundamental understanding, these are the ways in which I try to make progress on problems.
Curiosity and the beauty of mathematical arguments and tools remain a big motivation throughout my work.
Who is your role model?
There are several people whose achievements have greatly contributed to shape our research field and who remain a constant source of inspiration. László Lovász is certainly one of them. His work has impacted a broad range of areas. To name just one example, his celebrated graph theta number has found numerous extensions, from geometric sphere packing to bounds in quantum information. As of today, it still provides the only known efficient optimal coloring algorithm for perfect graphs, a landmark result in semidefinite optimization. I also want to mention Jean Lasserre and Pablo Parrilo, for their remarkable impact on the field of polynomial optimization: they realized that classical mathematical results about moment theory, positive polynomials and sums of squares could be combined with modern semidefinite optimization tools to design dedicated optimization methods. It is fascinating to see classical mathematics going back to the mathematician David Hilbert around 1900 becoming useful to address optimization challenges of today. The EOR department of Tilburg University has a strong group of researchers in these fields with whom I am very happy to be able to collaborate.