Zobrazeno 1 - 10
of 10 674
pro vyhledávání: '"Henrion"'
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 equ
Externí odkaz:
http://arxiv.org/abs/2412.07361
We study optimal control of PDEs under uncertainty with the state variable subject to joint chance constraints. The controls are deterministic, but the states are probabilistic due to random variables in the governing equation. Joint chance constrain
Externí odkaz:
http://arxiv.org/abs/2412.05125
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 moment-based optimal control of PDEs to consider a quadratic cost on the
Externí odkaz:
http://arxiv.org/abs/2411.11528
We introduce a variant of the D-optimal design of experiments problem with a more general information matrix that takes into account the representation of the design space S. The main motivation is that if S $\subset$ R d is the unit ball, the unit b
Externí odkaz:
http://arxiv.org/abs/2409.04058
We introduce an infinite-dimensional version of the Christoffel function, where now (i) its argument lies in a Hilbert space of functions, and (ii) its associated underlying measure is supported on a compact subset of the Hilbert space. We show that
Externí odkaz:
http://arxiv.org/abs/2407.02019
Autor:
Henrion, Didier
In these notes, the Christoffel-Darboux polynomial kernel is extended to infinite-dimensional Hilbert spaces, following as closely as possible its original finite-dimensional treatment.
Externí odkaz:
http://arxiv.org/abs/2407.01021
This article develops mathematical formalisms and provides numerical methods for studying the evolution of measures in nonsmooth dynamical systems using the continuity equation. The nonsmooth dynamical system is described by an evolution variational
Externí odkaz:
http://arxiv.org/abs/2405.09189
Two subsets of a given set are path-disconnected if they lie in different connected components of the larger set. Verification of path-disconnectedness is essential in proving the infeasibility of motion planning and trajectory optimization algorithm
Externí odkaz:
http://arxiv.org/abs/2404.06985
This paper develops a method to upper-bound extreme-values of time-windowed risks for stochastic processes. Examples of such risks include the maximum average or 90% quantile of the current along a transmission line in any 5-minute window. This work
Externí odkaz:
http://arxiv.org/abs/2404.06961
We describe a parametric univariate quadratic optimization problem for which the moment-SOS hierarchy has finite but increasingly slow convergence when the parameter tends to its limit value. We estimate the order of finite convergence as a function
Externí odkaz:
http://arxiv.org/abs/2403.08329