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Related papers: On the convergence of the Gaver-Stehfest algorithm

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In this note, we propose and study the notion of modified Fej\'{e}r sequences. Within a Hilbert space setting, we show that it provides a unifying framework to prove convergence rates for objective function values of several optimization…

Optimization and Control · Mathematics 2015-10-16 Junhong Lin , Lorenzo Rosasco , Silvia Villa , Ding-Xuan Zhou

We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…

Functional Analysis · Mathematics 2022-09-02 Soumyadip Ghosh , Yingdong Lu , Tomasz J. Nowicki

The development of efficient sampling algorithms catering to non-Euclidean geometries has been a challenging endeavor, as discretization techniques which succeed in the Euclidean setting do not readily carry over to more general settings.…

Data Structures and Algorithms · Computer Science 2025-12-24 Sivakanth Gopi , Yin Tat Lee , Daogao Liu , Ruoqi Shen , Kevin Tian

An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…

Machine Learning · Computer Science 2023-09-19 Abdelmouaiz Tebjou , Goran Frehse , Faïcel Chamroukhi

We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using level sets of a certain class of polynomials known as Christoffel functions. The level…

Systems and Control · Electrical Eng. & Systems 2021-04-29 Alex Devonport , Forest Yang , Laurent El Ghaoui , Murat Arcak

We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known…

Functional Analysis · Mathematics 2025-04-01 Joannis Alexopoulos

Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…

Artificial Intelligence · Computer Science 2013-02-28 Adriano Azevedo-Filho , Ross D. Shachter

We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact…

Optimization and Control · Mathematics 2024-06-24 Ewa Bednarczuk , Giovanni Bruccola , Gabriele Scrivanti , The Hung Tran

Equilibrium computation on Riemannian manifolds provides a unifying framework for numerous problems in machine learning and data analytics. One of the simplest yet most fundamental methods is Riemannian gradient descent (RGD). While its…

Optimization and Control · Mathematics 2025-11-11 Yang Cai , Michael I. Jordan , Tianyi Lin , Argyris Oikonomou , Emmanouil-Vasileios Vlatakis-Gkaragkounis

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

Optimization and Control · Mathematics 2025-03-11 Azar Louzi

This work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated as local random search algorithms, it is…

Systems and Control · Computer Science 2011-02-10 Chang-Ching Chen , Chia-Shiang Tseng , Che Lin

Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an…

Machine Learning · Statistics 2023-09-12 Katharina Ott , Michael Tiemann , Philipp Hennig , François-Xavier Briol

We study a stochastic anchored gradient scheme, namely HalpernSGD, which combines the classical Halpern iteration for finding a minimizer of a convex and $L$-smooth objective function with a stochastic {first-order} oracle. The algorithm is…

Optimization and Control · Mathematics 2026-03-24 Vittorio Colao , Katherine Rossella Foglia

The conformal method developed in the 1970s and the more recent Lagrangian and Hamiltonian conformal thin-sandwich methods are techniques for finding solutions of the Einstein constraint equations. We show that they are manifestations of a…

General Relativity and Quantum Cosmology · Physics 2015-06-18 David Maxwell

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

Optimization and Control · Mathematics 2020-11-03 Caroline Geiersbach , Estefania Loayza-Romero , Kathrin Welker

We prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of Hilbert spaces and the more general case of Banach spaces. The new ingredient of the paper is that we bound the…

Numerical Analysis · Mathematics 2023-04-14 V. N. Temlyakov

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

Computation · Statistics 2012-09-04 Björn Bornkamp

In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…

Optimization and Control · Mathematics 2023-03-01 Zijian Liu , Ta Duy Nguyen , Thien Hang Nguyen , Alina Ene , Huy Lê Nguyen

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

Optimization and Control · Mathematics 2020-02-25 Johannes O. Royset

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ