OC: Optimisation and Control

Presentation

The Optimisation and Control group focuses on decision making theory and in particular on three major research axes: optimisation, dynamical systems, and probability.
The group develops theory, algorithms and software for the analysis, the control, and the optimisation of different classes of systems, including dynamical and stochastic aspects. Its research is fundamentally rooted in several facets of mathematics, such as graph theory, mathematical programming, differential geometry, dynamical systems, (convex, non-smooth, and stochastic) analysis, linear algebra, probability, stochastic processes, as well as numerical methods. Several of our works live at the intersections of these domains. The group also applies its findings into many application domains, and its members have a variety of academic and industrial collaborations.

Keywords

Optimisation, dynamical systems, probability.

Applications domains

Cyber-physical systems, energy, transportation, health, logistics, planning, network problems, telecom, quantum computing, optimal control in aerospace application, neurophysiology, astrodynamics and gravitation, finance.

The following section presents the team's research themes.

Continuous Optimization, Dynamical systems, Data science

Work in this domain is centered around convex, non-convex and vector continuous optimisation, especially in the context of building first-order algorithms for the resolution of optimisation problems of possibly large dimension. Special emphasis is put into looking at the algorithms from a dynamical system perspective and at cases in which the optimisation problems themselves change over time.
Recently, we are exploring the interplay between optimisation and data science, especially for cases in which the cost or the constraints must be inferred from data.

Keywords

Convex optimisation, proximal point methods, vector optimization, generalised convexity, nonsmooth optimization, online algorithms, time-varying optimization, learning and user’s preferences.

Applications

Cyber-physical and social systems (energy, transportation, health), signal processing.

Combinatorial optimization, Operations Research, Data science

Work in this domain is centred around the formulation and resolution techniques for combinatorial (discrete) optimisation problems stemming from operations research applications. These problems are typically linear, quadratic, or polynomial optimisation problems with integer decision variables. Particular care is put in the formulation and re-formulation of problems to obtain better theoretical guarantees, the study of complexity, decomposition algorithms (e.g., branch and cut, Benders) and heuristics, as well as the robustness and sensitivity of the solution to parameter changes.

Recently, we are exploring the interplay between combinatorial optimisation and data science, especially when they can help one another: in one direction as offering certificates of explainability of certain machine learning models, and in the other direction as techniques to learn how to optimise hard combinatorial problems. Very recently, we are exploring the interplay between combinatorial optimisation and quantum computing.

Keywords

Combinatorial discrete optimisation, complexity theory, integer optimisation problems, linear, quadratic, and polynomial optimisation with integer variables, QUBO, decomposition methods, robustness, learning to optimise, decision trees.

Applications

Logistics, network problems, planning, smart energy and transportation, telecom, text analysis, quantum computing.

Dynamical systems, Geometric control, Dynamics of the universe

Work in this domain is centered around two main axes: geometric control and astrodynamics. For the former, we are interested in the theory of non-linear control, and specifically geometric control. Here the aim is to tackle control problems via differential geometry, with a special emphasis in sub-Riemannian geometry. For the latter, we are interested in dynamical systems under gravitational laws, with special emphasis to classical and relativistic gravitation, the dynamics of globular clusters, galaxies, the theory of isochrone oscillations, and the dynamics of the entire universe.

Keywords

Geometric control, sub-Riemannian geometry, non-holonomic systems, Inverse control problems, classical and relativistic gravitation, the dynamics of globular clusters, galaxies, the theory of isochrone oscillations, the dynamics of the universe.

Applications

Optimal control in aerospace application (e.g., rocket re-entry), neurophysiology, theoretical astrophysics.

Stochastic Analysis and Control