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Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the…

Numerical Analysis · Mathematics 2015-11-19 Federica Porta , Marco Prato , Luca Zanni

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

Optimization and Control · Mathematics 2022-10-12 Pierre-Cyril Aubin-Frankowski , Anna Korba , Flavien Léger

Transparent and reflective objects in everyday environments pose significant challenges for depth sensors due to their unique visual properties, such as specular reflections and light transmission. These characteristics often lead to…

Robotics · Computer Science 2025-06-12 Guanghu Xie , Zhiduo Jiang , Yonglong Zhang , Yang Liu , Zongwu Xie , Baoshi Cao , Hong Liu

This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…

Numerical Analysis · Mathematics 2023-01-04 Eleonora Denich , Paolo Novati , Stefano Picotti

This paper presents a comprehensive convergence analysis for the mirror descent (MD) method, a widely used algorithm in convex optimization. The key feature of this algorithm is that it provides a generalization of classical gradient-based…

Optimization and Control · Mathematics 2024-09-16 Mengmou Li , Khaled Laib , Takeshi Hatanaka , Ioannis Lestas

Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in $H^{1}$ norm for deep Ritz methods for Laplace equations with Dirichlet boundary…

Numerical Analysis · Mathematics 2021-11-04 Chenguang Duan , Yuling Jiao , Yanming Lai , Xiliang Lu , Qimeng Quan , Jerry Zhijian Yang

This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…

Analysis of PDEs · Mathematics 2021-06-25 Philippe Laurent , Guillaume Legendre , Julien Salomon

This paper studies a broadband orthogonal frequency division multiplexing (OFDM) system aided by a beyond diagonal intelligent reflecting surface (BD-IRS), where inter-connections exist among different elements such that the reflection…

Information Theory · Computer Science 2025-09-09 Ye Yuan , Shuowen Zhang

In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) algorithm and the Frank-Wolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the…

Optimization and Control · Mathematics 2021-06-09 R. Díaz Millán , O. P. Ferreira , J. Ugon

Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence…

Differential Geometry · Mathematics 2025-08-06 David Glickenstein , Lee Sidbury

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact…

Optimization and Control · Mathematics 2019-04-25 M. Marques Alves , Jonathan Eckstein , Marina Geremia , Jefferson Melo

Intelligent reflecting surface (IRS) has been considered as an efficient way to boost the computation capability of mobile edge computing (MEC) system, especially when the communication links is blocked or the communication signal is weak.…

Information Theory · Computer Science 2024-07-16 N. Li , W. Hao , X. Li , Z. Zhu , Z. Tang , S. Yang

We consider distributed optimization in the client-server setting. By use of Douglas-Rachford splitting to the dual of the sum problem, we design a BFGS method that requires minimal communication (sending/receiving one vector per round for…

Optimization and Control · Mathematics 2024-10-30 Dingran Yi , Nikolaos M. Freris

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to…

Machine Learning · Computer Science 2012-10-19 Sridhar Mahadevan , Bo Liu

Recent works in Reinforcement Learning (RL) combine model-free (Mf)-RL algorithms with model-based (Mb)-RL approaches to get the best from both: asymptotic performance of Mf-RL and high sample-efficiency of Mb-RL. Inspired by these works,…

Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…

Machine Learning · Computer Science 2024-10-21 Shuyang Wang , Diego Klabjan

We propose a novel approach to the inverse Ising problem which employs the recently introduced Density Consistency approximation (DC) to determine the model parameters (couplings and external fields) maximizing the likelihood of given…

Statistical Mechanics · Physics 2021-04-01 Alfredo Braunstein , Giovanni Catania , Luca Dall'Asta , Anna Paola Muntoni

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex…

Optimization and Control · Mathematics 2018-02-07 Robert Hesse , D. Russell Luke , Patrick Neumann

Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…

Optimization and Control · Mathematics 2015-07-09 Damek Davis

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…

Optimization and Control · Mathematics 2014-04-18 Radu Ioan Bot , Ernö Robert Csetnek