Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy
Analysis of PDEs
2025-07-08 v4 Optimization and Control
Abstract
We prove that there is no relaxation gap between a quasi-dissipative nonlinear evolution equation in a Hilbert space and its linear Liouville equation reformulation on probability measures. In other words, strong and generalized solutions of such equations are unique in the class of measure-valued solutions. As a major consequence, non-convex numerical optimization over these non-linear partial differential equations can be carried out with the infinite-dimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity.
Keywords
Cite
@article{arxiv.2412.07361,
title = {Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy},
author = {Saroj Prasad Chhatoi and Didier Henrion and Swann Marx and Nicolas Seguin},
journal= {arXiv preprint arXiv:2412.07361},
year = {2025}
}