5 papers
Concentration of measure-valued solutions for semilinear parabolic equations
Charlie Lebarbé, Ãmilien 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 KružÃk +1
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…
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…
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…