相关论文: Geometric linearisation for optimal transport with…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is…
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated optimal…
Given two probability measures $\mu$ and $\nu$ in "convex order" on $\R^d$, we study the profile of one-step martingale plans $\pi$ on $\R^d\times \R^d$ that optimize the expected value of the modulus of their increment among all…
In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method…
We use the geometry of suitably generalised potentials to solve risk-sensitive Markovian optimal stopping problems. As in the linear case due to Dynkin and Yushkievich (1967), the value function is the pointwise infimum of those functions…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
In this paper, we introduce a class of nonsmooth nonconvex least square optimization problem using convex analysis tools and we propose to use the iterative minimization-majorization (MM) algorithm on a convex set with initializer away from…
We consider the space of probability measures on a discrete set $X$, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset $Y \subseteq X$, it is natural to ask whether they can be connected…
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
The scope of this note is to make a self-contained survey of the recent developments and achievements of the theory of L1-Optimal Transportation on metric measure spaces. Among the results proved in the recent papers [20, 21] where the…
We consider Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…