Kinetic Langevin MCMC sampling without gradient Lipschitz continuity - the strongly convex case
In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to sample ...
Sharp lower bounds on the manifold widths of Sobolev and Besov spaces
We study the manifold n-widths of Sobolev and Besov spaces with error measured in the L p-norm. The manifold widths measure how efficiently these spaces can be approximated by continuous non-linear parametric methods. Existing upper and lower ...
Adaptive Huber trace regression with low-rank matrix parameter via nonconvex regularization
In this paper, we consider the adaptive Huber trace regression model with matrix covariates. A non-convex penalty function is employed to account for the low-rank structure of the unknown parameter. Under some mild conditions, we establish an ...
Interpolation by decomposable univariate polynomials
The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two polynomials of ...
On the complexity of strong approximation of stochastic differential equations with a non-Lipschitz drift coefficient
We survey recent developments in the field of complexity of pathwise approximation in p-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion. First, we ...
Randomized complexity of mean computation and the adaption problem
Recently the adaption problem of Information-Based Complexity (IBC) for linear problems in the randomized setting was solved in Heinrich (2024) [8]. Several papers treating further aspects of this problem followed. However, all examples obtained ...
Minimal dispersion on the cube and the torus
We improve some upper bounds for minimal dispersion on the cube and torus. Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random and non-...
An ultra-weak space-time variational formulation for the Schrödinger equation
We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schrödinger equation with an instationary Hamiltonian. We prove optimal inf-sup stability and introduce a space-time Petrov-...