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7 papers
The gap between a variational problem and its occupation measure relaxation
Milan Korda, Rodolfo Rios-Zertuche
Recent works have proposed linear programming relaxations of variational optimization problems subject to nonlinear PDE constraints based on the occupation measure formalism. The m…
Global optimization of low-rank polynomials
Llorenç Balada Gaggioli, Didier Henrion, Milan Korda
This work considers polynomial optimization problems where the objective admits a low-rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimiza…
Polynomial argmin for recovery and approximation of multivariate discontinuous functions
Didier Henrion, Milan Korda, Jean-Bernard Lasserre
We propose to approximate a (possibly discontinuous) multivariate function f (x) on a compact set by the partial minimizer arg miny p(x, y) of an appropriate polynomial p whose con…
Solving unbounded optimal control problems with the moment-SOS hierarchy *
Karolına Sehnalová, Didier Henrion, Milan Korda +1
The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution foc…
Optimal Control of 1D Semilinear Heat Equations with Moment-SOS Relaxations
Charlie Lebarbé, Emilien Flayac, Michel Fournié +2
We use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of mo…
Clarifying the effect of mean subtraction on Dynamic Mode Decomposition
Gowtham S Seenivasaharagavan, Milan Korda, Hassan Arbabi +1
Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven ap…