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In this paper, we revisit a well-known distributed projected subgradient algorithm which aims to minimize a sum of cost functions with a common set constraint. In contrast to most of existing results, weight matrices of the time-varying…

Optimization and Control · Mathematics 2021-04-29 Weijian Li , Zihan Chen , Youcheng Lou , Yiguang Hong

In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in [Bai, et al. Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as its linear…

Numerical Analysis · Mathematics 2019-06-20 Jianchao Bai , Xiaokai Chang , Jicheng Li , Fengmin Xu

In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection-algorithm,…

Optimization and Control · Mathematics 2020-10-02 Le Hai Yen , Le Dung Muu

We study the convergence rate of the Circumcentered-Reflection Method (CRM) for solving the convex feasibility problem and compare it with the Method of Alternating Projections (MAP). Under an error bound assumption, we prove that both…

Optimization and Control · Mathematics 2021-05-04 Reza Arefidamghani , Roger Behling , Yunier Bello-Cruz , Alfredo N. Iusem , Luiz-Rafael Santos

This paper presents a fast spectral unmixing algorithm based on Dykstra's alternating projection. The proposed algorithm formulates the fully constrained least squares optimization problem associated with the spectral unmixing task as an…

Computer Vision and Pattern Recognition · Computer Science 2015-05-08 Qi Wei , Jose Bioucas-Dias , Nicolas Dobigeon , Jean-Yves Tourneret

We study the convergence of specific inexact alternating projections for two non-convex sets in a Euclidean space. The $\sigma$-quasioptimal metric projection ($\sigma \geq 1$) of a point $x$ onto a set $A$ consists of points in $A$ the…

Optimization and Control · Mathematics 2025-09-09 Stanislav Budzinskiy

Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in a Euclidean space.…

Dynamical Systems · Mathematics 2012-02-02 Roberto Tron , Bijan Afsari , René Vidal

Calculating averages with respect to probability measures on submanifolds is often necessary in various application areas such as molecular dynamics, computational statistical mechanics and Bayesian statistics. In recent years, various…

Numerical Analysis · Mathematics 2021-06-30 Upanshu Sharma , Wei Zhang

Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…

Discrete Mathematics · Computer Science 2021-12-14 Gabriela Cristescu , Vlad-Florin Dragoi , Sorin-Horatiu Hoara

We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…

Mathematical Software · Computer Science 2019-03-08 Bas Peters , Felix J. Herrmann

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

Computer Vision and Pattern Recognition · Computer Science 2020-07-07 Wei Lian , WangMeng Zuo , Lei Zhang

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…

Optimization and Control · Mathematics 2019-02-13 Tao Sun , Dongsheng Li , Hao Jiang , Zhe Quan

We consider sequences $(B_k)_{k=0}^\infty$ of points obtained by projecting back and forth between two manifolds $\M_1$ and $\M_2$, and give conditions guaranteeing that the sequence converge to a limit $B_\infty\in\M_1\cap\M_2$. Our…

Numerical Analysis · Mathematics 2011-07-21 Fredrik Andersson , Marcus Carlsson

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

Computer Vision and Pattern Recognition · Computer Science 2015-12-03 Xiaowei Zhou , Menglong Zhu , Kostas Daniilidis

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…

Machine Learning · Statistics 2016-09-13 Subhaneil Lahiri , Peiran Gao , Surya Ganguli

The von Neumann-Halperin method of alternating projections converges strongly to the projection of a given point onto the intersection of finitely many closed affine subspaces. We propose acceleration schemes making use of two ideas:…

Optimization and Control · Mathematics 2014-07-17 C. H. Jeffrey Pang

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Optimization and Control · Mathematics 2020-08-31 Zheng Zhou , Bing Tan , Songxiao Li

In this paper, we investigate the attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual…

Optimization and Control · Mathematics 2018-01-18 Franck Iutzeler , Jerome Malick

Consensus on nonlinear spaces is of use in many control applications. This paper proposes a gradient descent flow algorithm for consensus on hypersurfaces. We show that if an inequality holds, then the system converges for almost all…

Optimization and Control · Mathematics 2020-04-02 Johan Markdahl

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…

Optimization and Control · Mathematics 2019-11-12 Aviv Gibali , Karl-Heinz Küfer , Daniel Reem , Philipp Süss