Missions

The project objective is to overcome the significant scalability barriers of the moment-sum-of-squares (moment-SOS) hierarchy, a powerful tool for solving non-linear, non-convex optimization problems.

Activities

The project will focus specifically on networked dynamical systems governed by nonlinear hyperbolic partial differential equations (PDEs). These models are crucial for applications like managing gas pipelines, traffic flow, and telecommunication networks. Our approach is to exploit the sparse network structure to decompose large-scale problems and leverage the theory of measure-valued solutions to handle the PDE dynamics without discretization.

The project will focus specifically on networked dynamical systems governed by nonlinear hyperbolic partial differential equations (PDEs). These models are crucial for applications like managing gas pipelines, traffic flow, and telecommunication networks. Our approach is to exploit the sparse network structure to decompose large-scale problems and leverage the theory of measure-valued solutions to handle the PDE dynamics without discretization.

Skills

We are looking for a candidate with a PhD in Applied Mathematics, Control Theory, Optimization, or a related field. The position is flexible and can be tailored to the profiles:
- Analysis-Oriented: Strong theoretical background in functional analysis, measure theory, and convex optimization. Experience with the moment-SOS hierarchy. Expertise in PDE theory (especially hyperbolic conservation laws) is a significant plus.
- Computation-Oriented: Strong background in numerical methods for optimization, especially semidefinite programming (SDP). Experience with numerical linear algebra, polynomial bases, and code development (e.g., in Julia, Matlab, or Python). Knowledge of techniques for exploiting numerical structure (sparsity, low-rank) is highly desirable.

Work Context

The MONET project is a bilateral collaboration between LAAS-CNRS (France) and FAU Erlangen-Nürnberg (Germany).

The position is located in a sector under the protection of scientific and technical potential (PPST), and therefore requires, in accordance with the regulations, that your arrival is authorized by the competent authority of the MESR.