相关论文: Abstract strongly convergent variants of the proxi…

We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…

Information divergences allow one to assess how close two distributions are from each other. Among the large panel of available measures, a special attention has been paid to convex $\varphi$-divergences, such as Kullback-Leibler,…

The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…

The authors in (Banjac et al., 2019) recently showed that the Douglas-Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive…

Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…

Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties:…

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator…

We propose conformal hyperrectangular prediction regions for multi-target regression. We propose split conformal prediction algorithms for both point and quantile regression to form hyperrectangular prediction regions, which allow for easy…

Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular,…

We leverage the proximal Galerkin algorithm (Keith and Surowiec, Foundations of Computational Mathematics, 2024, DOI: 10.1007/s10208-024-09681-8), a recently introduced mesh-independent algorithm, to obtain a high-order finite element…

We analyze weak convergence on CAT(0) spaces and the existence and properties of corresponding weak topologies.

This paper provides a new way of developing the splitting method which is used to solve the problem of finding the resolvent of the sum of maximal monotone operators in Hilbert spaces. By employing accelerated techniques developed by Davis…

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…

This paper proposes novel primal-dual dynamical systems for solving linear equality constrained convex optimization. First, we introduce a primal-dual dynamical system with implicit Hessian damping, which can neutralize the transversal…

In a Hilbert framework, for convex differentiable optimization, we consider accelerated gradient methods obtained by combining temporal scaling and averaging techniques with Tikhonov regularization. We start from the continuous steepest…

We study weak convergence of a sequence of point processes to a scale-invariant simple point process. For a deterministic sequence $(z_n)_{n\in\mathbb{N}}$ of positive real numbers increasing to infinity as $n \to \infty$ and a sequence…

This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theoretical framework for inexact proximal point (IPP) methods…

We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…