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In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…

Optimization and Control · Mathematics 2020-06-18 Assalé Adjé

We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the…

Information Theory · Computer Science 2024-01-31 Farhang Yeganegi , Arian Eamaz , Mojtaba Soltanalian

The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence…

Numerical Analysis · Mathematics 2020-06-03 Riley Borgard , Steven N. Harding , Haley Duba , Chloe Makdad , Jay Mayfield , Randal Tuggle , Eric Weber

We propose a new deterministic Kaczmarz algorithm for solving consistent linear systems $A\mathbf{x}=\mathbf{b}$. Basically, the algorithm replaces orthogonal projections with reflections in the original scheme of Stefan Kaczmarz. Building…

Numerical Analysis · Mathematics 2023-05-17 Changpeng Shao

This paper proposes an off-line algorithm, called Recurrent Model Predictive Control (RMPC), to solve general nonlinear finite-horizon optimal control problems. Unlike traditional Model Predictive Control (MPC) algorithms, it can make full…

Systems and Control · Electrical Eng. & Systems 2021-02-24 Zhengyu Liu , Jingliang Duan , Wenxuan Wang , Shengbo Eben Li , Yuming Yin , Ziyu Lin , Qi Sun , Bo Cheng

In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of…

Systems and Control · Computer Science 2011-11-09 Saikat Chatterjee , Dennis Sundman , Mikko Vehkaperä , Mikael Skoglund

Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed…

Optimization and Control · Mathematics 2020-12-21 Yue Yu , Purnanand Elango , Behçet Açikmeşe

In this note we compare the randomized extended Kaczmarz (EK) algorithm and randomized coordinate descent (CD) for solving the full-rank overdetermined linear least-squares problem and prove that CD needs less operations for satisfying the…

Numerical Analysis · Mathematics 2014-09-02 Bogdan Dumitrescu

The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of…

Numerical Analysis · Mathematics 2024-06-24 Ze Wang , Jun-Feng Yin , Ji-Chen Zhao

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Optimization and Control · Mathematics 2012-09-19 Bart Vandereycken

The block Kaczmarz method and its variants are designed for solving the over-determined linear system. They involve iteratively projecting the current point onto the solution space of a subset of constraints. In this work, by alternately…

Numerical Analysis · Mathematics 2023-11-02 Nian-Ci Wu , Yang Zhou , Zhaolu Tian

The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…

Numerical Analysis · Mathematics 2014-09-04 Jonathan Briskman , Deanna Needell

The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for…

Optimization and Control · Mathematics 2023-07-31 Dirk A. Lorenz , Maximilian Winkler

The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…

Numerical Analysis · Mathematics 2022-10-18 Lionel Tondji , Dirk A Lorenz

X-ray computed tomography (CT) plays a key role in digitizing three-dimensional structures for a wide range of medical and industrial applications. Traditional CT systems often rely on standard circular and helical scan trajectories, which…

Robotics · Computer Science 2024-02-19 Linda-Sophie Schneider , Gabriel Herl , Andreas Maier

In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the…

Functional Analysis · Mathematics 2013-11-20 Jonathan M. Borwein , Guoyin Li , Liangjin Yao

We investigate the randomized Kaczmarz method that adaptively updates the stepsize using readily available information for solving inconsistent linear systems. A novel geometric interpretation is provided which shows that the proposed…

Numerical Analysis · Mathematics 2023-03-17 Yun Zeng , Deren Han , Yansheng Su , Jiaxin Xie

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

Machine Learning · Statistics 2020-03-23 Xiaojun Mao , Raymond K. W. Wong , Song Xi Chen

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…

Optimization and Control · Mathematics 2013-08-21 Yair Censor , Ran Davidi , Gabor T. Herman , Reinhard W. Schulte , Luba Tetruashvili

With increasing concerns about security, the need for highly secure physical biometrics-based authentication systems utilizing \emph{cancelable biometric} technologies is on the rise. Because the problem of cancelable template generation…

Computer Vision and Pattern Recognition · Computer Science 2015-05-22 Devansh Arpit , Ifeoma Nwogu , Gaurav Srivastava , Venu Govindaraju