6 papers
Bounding extreme events in dynamical systems over an infinite time horizon
Karol\'ına Sehnalová, Milan Korda
This work addresses the computation of extreme values of observables along trajectories of dynamical systems over an \ks{infinite time horizon}. The setting is intrinsically global…
Concentration of measure-valued solutions for semilinear parabolic equations
Charlie Lebarbé, Émilien Flayac, Michel Fournié +2
The moment-sum-of-squares hierarchy provides a powerful framework for solving non-convex optimal control problems by constructing a sequence of convex semidefinite relaxations. How…
Composition and tensor train structure in polynomial optimization
Llorenç Balada Gaggioli, Didier Henrion, Milan Korda
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to inte…
Semidefinite relaxations for nonlinear elasticity with energies convex in the Cauchy-Green strain tensor
Didier Henrion, Milan Korda, Martin Kružík +2
In nonlinear elasticity, finding the deformation of a material which minimizes a given stored energy density is a challenging calculus of variations problem which may fail to have…
Sufficient conditions for the absence of relaxation gaps in state-constrained optimal control
Nicolas Augier, Milan Korda, Rodolfo Rios-Zertuche
This work presents new sufficient conditions for the absence of a gap corresponding to Young measure and occupation measure relaxations for constrained optimal control problems. Un…
Young measure relaxation gaps for controllable systems with smooth state constraints
Nicolas Augier, Milan Korda, Rodolfo Rios-Zertuche
In this article, we tackle the problem of the existence of a gap corresponding to Young measure relaxations for state-constrained optimal control problems. We provide a counterexam…