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2026-10-06 (14:00) : Newcomers Seminar

At Euler building (room A.002)

Duration: 60 minutes

Organized by Mathematical Engineering

Section 1: Anthony Couthures

Speaker : Anthony Couthures (UCLouvain)

Anthony Couthures

Anthony Couthures is a Postdoctoral Researcher at the ICTEAM Institute at UCLouvain, Belgium, where he develops optimization-based tools for the performance analysis of control systems. He received his Ph.D. in automatic control from Université de Lorraine in 2026, researching the influence of opinion dynamics on climate change. His broader interests include nonlinear multi-agent systems, game theory, and optimization, particularly applied to coupled socio-environmental systems.I will first discuss my Ph.D. research at Université de Lorraine on multi-agent systems and environmental modeling. I will give a high-level introduction to opinion dynamics and explain how I used game theory and network approaches to model the feedback loop between social polarization and climate change negotiations, investigating phenomena like the "oscillatory tragedy of the commons." Next, I will introduce my current postdoctoral work with Julien M. Hendrickx and Gianluca Bianchin on robust control and optimization. We are adapting the Performance Estimation Problem (PEP) framework, which was originally developed for analyzing optimization algorithms, to evaluate control systems. I will show how we use this framework to quantify the exact finite-horizon robustness of Linear Quadratic Regulators (LQR) under LTI uncertainties by reformulating the worst-case search as a Semidefinite Program (SDP).

Abstract : I will first discuss my Ph.D. research at Université de Lorraine on multi-agent systems and environmental modeling. I will give a high-level introduction to opinion dynamics and explain how I used game theory and network approaches to model the feedback loop between social polarization and climate change negotiations, investigating phenomena like the "oscillatory tragedy of the commons." Next, I will introduce my current postdoctoral work with Julien M. Hendrickx and Gianluca Bianchin on robust control and optimization. We are adapting the Performance Estimation Problem (PEP) framework, which was originally developed for analyzing optimization algorithms, to evaluate control systems. I will show how we use this framework to quantify the exact finite-horizon robustness of Linear Quadratic Regulators (LQR) under LTI uncertainties by reformulating the worst-case search as a Semidefinite Program (SDP).

Section 2: Manifolds everywhere: from derivative-free optimization to data fitting.

Speaker : Sacha Benarroch (UCLouvain)

Abstract : This talk is in two parts. First, a known limitation of direct search algorithms for derivative-free optimization is that of solving problems with equality constraints. This talk investigates the use of Riemannian optimization tools to solve derivative-free problems in the case where the feasible set for equality constraints makes up a Riemannian submanifold of R^n. Theoretical and practical performance of the obtained feasible method are addressed. Leaving the realm of optimization, the talk then moves on to Riemannian data fitting. While methods to interpolate manifold-valued data exist, they suffer from some shortcomings, typically restrictive assumptions about the so-called data sites and approximations due to the use of Euclidean data fitting techniques on the tangent spaces. The second part of this talk provides an overview of these shortcomings and somes avenues to address them.

Section 3: Sum-of-Squares Programming via Optimization on Manifolds

Speaker : Charles Van Hees (UCLouvain)

Abstract : For decades, the nonnegativity of polynomials has been of concern to mathematicians across several fields: global optimization, control theory, probability, etc. Nevertheless, in the general case, determining whether a polynomial is nonnegative or not is a NP-hard problem. For univariate polynomials however, nonnegativity is equivalent to being a sum of two squares: there exist two polynomials such that the sum of their squares equals the given polynomial. A few years ago, Legat et al. derived an algorithm for finding a sum-of-squares decomposition of a univariate polynomial satisfying a set of linear constraints. The novel contribution of this Master’s thesis is the introduction of a linear objective we aim to minimize. This problem is traditionally modelled as an SDP and solved using, for instance, an Interior Point Method. However, SDPs quickly become intractable due to the number of variables, which grows quadratically in the size of the problem. Hence, we rely on an idea proposed by Burer and Monteiro at the beginning of the 21st century, by considering an equivalent nonlinear formulation whose variables are the two polynomials of the sum-of-squares decomposition. While introducing nonconvexity, it drastically reduces the size of the problem. Among the various methods that exist to solve such problems (Augmented Lagrangian, Projected Gradient, etc.), we opted for an approach based on manifolds. We derive a first-order Riemannian optimization algorithm that can be used when the feasible set is a smooth manifold. Although the feasible set is surprisingly smooth in many cases (when the constraint operator is bijective, or near pairs of polynomials sharing at most one common root), it turns out that it is not a smooth manifold for every set of linear constraints defining it.

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