Zobrazeno 1 - 10
of 7 622
pro vyhledávání: '"A. Henrion"'
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
Autor:
Henrion, Didier, Rudi, Alessandro
Using standard tools of harmonic analysis, we state and solve the problem of moments for positive measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approx
Externí odkaz:
http://arxiv.org/abs/2401.07734
This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of infinite-dimensional l
Externí odkaz:
http://arxiv.org/abs/2401.00815
Autor:
Henrion, Didier
The moment-SOS (sum of squares) hierarchy is a powerful approach for solving globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of
Externí odkaz:
http://arxiv.org/abs/2310.17229