相关论文: How to quantise probabilities while preserving the…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
In this paper, we consider constrained optimization problems with convex, smooth objective and constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class…
This paper introduces a numerical algorithm to compute the $L_2$ optimal transport map between two measures $\mu$ and $\nu$, where $\mu$ derives from a density $\rho$ defined as a piecewise linear function (supported by a tetrahedral mesh),…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are…
We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…
We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…
We propose a simple, stable and distributed algorithm which directly optimizes the nonconvex maximum likelihood criterion for sensor network localization, with no need to tune any free parameter. We reformulate the problem to obtain a…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…