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We study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth Banach spaces. For Banach spaces which are convex and smooth of power type,…

Functional Analysis · Mathematics 2020-10-09 Christian Bargetz , Emir Medjic

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…

Optimization and Control · Mathematics 2022-09-27 Shota Takahashi , Mituhiro Fukuda , Mirai Tanaka

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…

Computer Vision and Pattern Recognition · Computer Science 2023-03-01 Aniket Pramanik , M. Bridget Zimmerman , Mathews Jacob

The sketch-and-project, as a general archetypal algorithm for solving linear systems, unifies a variety of randomized iterative methods such as the randomized Kaczmarz and randomized coordinate descent. However, since it aims to find a…

Numerical Analysis · Mathematics 2022-05-04 Ziyang Yuan , Lu Zhang , Hongxia Wang , Hui Zhang

It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life, to address this issue, we studied…

General Mathematics · Mathematics 2024-04-01 Lawan Bulama Mohammed , Adem Kilicman

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…

Optimization and Control · Mathematics 2009-05-12 Shiqian Ma , Donald Goldfarb , Lifeng Chen

We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…

Computer Vision and Pattern Recognition · Computer Science 2012-08-13 Yao Lu , Kaizhu Huang , Cheng-Lin Liu

Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…

Optimization and Control · Mathematics 2025-04-10 Keiichi Morikuni , Koya Sakakibara , Asuka Takatsu

A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…

Optimization and Control · Mathematics 2014-08-15 C. H. Jeffrey Pang

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…

Optimization and Control · Mathematics 2009-11-04 Augusto Ferrante , Federico Ramponi , Francesco Ticozzi

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…

Machine Learning · Computer Science 2020-10-01 Frank Nielsen , Richard Nock

The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…

Machine Learning · Computer Science 2025-04-11 Tuyen Pham , Hana Dal Poz Kouřimská , Hubert Wagner

In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…

Optimization and Control · Mathematics 2015-11-13 J. G. Barrios , J. Y. Bello Cruz , O. P. Ferreira , S. Z. Németh

The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…

Optimization and Control · Mathematics 2015-06-30 C. H. Jeffrey Pang

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

Functional Analysis · Mathematics 2014-05-22 Ibrahim Karahan , Murat Ozdemir

This work analyzes the inverse optimal transport (IOT) problem under Bregman regularization. We establish well-posedness results, including existence, uniqueness (up to equivalence classes of solutions), and stability, under several…

Optimization and Control · Mathematics 2026-05-01 Chenglong Bao , Zanyu Li , Yunan Yang

Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…

Optimization and Control · Mathematics 2019-11-21 Cyrille W. Combettes , Sebastian Pokutta

We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality,…

Optimization and Control · Mathematics 2024-12-13 Waïss Azizian , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…

Optimization and Control · Mathematics 2017-09-19 Nguyen Hieu Thao

This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…

Optimization and Control · Mathematics 2024-05-28 Peter Richtárik , Abdurakhmon Sadiev , Yury Demidovich