Related papers: Optimal Bregman quantization : existence and uniqu…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
We study the logarithmic $L^{(\alpha)}$-divergence which extrapolates the Bregman divergence and corresponds to solutions to novel optimal transport problems. We show that this logarithmic divergence is equivalent to a conformal…
In a series of papers on optimal control problems for the monodomain as well as for the bidomain equations of cardiac electrophysiology, the authors studied existence of minimizers and derived first-order necessary optimality conditions.…
In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional…
In this paper, we study constraint minimizers $u$ of the planar Schr\"odinger-Poisson system with a logarithmic convolution potential $\ln |x|\ast u^2$ and a logarithmic external potential $V(x)=\ln (1+|x|^2)$, which can be described by the…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…
This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the $L^r$-Kantorovich (or transport) distance, where either the locations or the weights of the approximations' atoms are…
Given a channel having binary input X = (x_1, x_2) having the probability distribution p_X = (p_{x_1}, p_{x_2}) that is corrupted by a continuous noise to produce a continuous output y \in Y = R. For a given conditional distribution…
In this paper, we prove an $L^2$ extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known $L^2$ extension theorems. As applications, we give proofs of a conjecture of Suita on…
Let $X$ be a normal variety. Assume that for some reduced divisor $D \subset X$, logarithmic 1-forms defined on the snc locus of $(X, D)$ extend to a log resolution $\tilde X \to X$ as logarithmic differential forms. We prove that then the…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model…
We give a new proof of the Caffarelli contraction theorem, which states that the Brenier optimal transport map sending the standard Gaussian measure onto a uniformly log-concave probability measure is Lipschitz. The proof combines a recent…
In this work, we extend some quantities introduced in "Optimization of conditional value-at-risk" of R.T Rockafellar and S. Uryasev to the case where the proximity between real numbers is measured by using a Bregman divergence. This leads…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
We study nonconvex homogeneous quadratically constrained quadratic optimization with one or two constraints, denoted by (QQ1) and (QQ2), respectively. (QQ2) contains (QQ1), trust region subproblem (TRS) and ellipsoid regularized total least…
We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants of strong unicity, for the problem of best uniform approximation with bounded coefficients, as first considered by Roulier and…
It is proved in Chon{\'e} and Le Meur (2001) that the problem of minimizing a Dirichlet-like functional of the function $u\_h$ discretized with $P\_1$ Finite Elements, under the constraint that $u\_h$ be convex, cannot converge. Here, we…