Weijia Wang
Weijia Wang is a PhD student in the PolSys team of LIP6, Sorbonne Université, and in the Sierra team at Inria Paris. His research centers on designing computer algebra-based algorithms to automate the convergence analysis of first-order optimization algorithms.
Session
Parametric linear matrix inequalities (LMIs) arise in optimization and control. A key question, motivated by the automation of convergence analysis of numerical optimization schemes, is to understand how their feasibility depends on parameters. In this talk, I present an approach that turns parametric LMI feasibility into parametric polynomial equations with constraints. The resulting parameter space can then be analyzed using real root classification based on Hermite's quadratic forms. I will show how this approach is implemented in Julia (notably Nemo.jl and AlgebraicSolving.jl, with real-geometry backends where appropriate), with efficient techniques such as multivariate rational interpolation. Finally, I will show that our implementation cleanly detects regions of parameter space where convergence properties change, for parametric LMIs arising from convergence analyses of first-order optimization methods.