Related papers: Forward-Backward Splitting with Bregman Distances
The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…
We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance…
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental…
Proximal gradient methods are a popular tool for the solution of structured, nonsmooth minimization problems. In this work, we investigate an extension of the former to general Banach spaces and provide worst-case convergence rates for,…
Over the past years, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper, we consider the Forward--Douglas--Rachford splitting method (FDR) [10,40], and study…
We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We…
We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…
We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a…
This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…
Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for…
Stochastic optimization powers the scalability of modern artificial intelligence, spanning machine learning, deep learning, reinforcement learning, and large language model training. Yet, existing theory remains largely confined to Hilbert…
In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…
We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error measures expressing the distance between exact and…