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In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Computer Vision and Pattern Recognition · Computer Science 2020-03-13 Pawan Goyal , Hussam Al Daas , Peter Benner

This work extends a previous study that introduced an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its objective is to address the limitations of the earlier approach. The reversible Kalman filter…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Svyatoslav Covanov , Cedric Pradalier

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…

Machine Learning · Statistics 2015-03-17 Ryota Tomioka , Kohei Hayashi , Hisashi Kashima

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…

Optimization and Control · Mathematics 2017-02-01 Alp Yurtsever , Bang Cong Vu , Volkan Cevher

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…

Optimization and Control · Mathematics 2015-07-10 Tianyi Lin , Shiqian Ma , Shuzhong Zhang

In this study, we investigate the problem of min-max continuous optimization in a black-box setting $\min_{x} \max_{y}f(x,y)$. A popular approach updates $x$ and $y$ simultaneously or alternatingly. However, two major limitations have been…

Neural and Evolutionary Computing · Computer Science 2022-04-07 Atsuhiro Miyagi , Kazuto Fukuchi , Jun Sakuma , Youhei Akimoto

Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…

Optimization and Control · Mathematics 2026-01-29 Runyu Zhang , Arvind Raghunathan , Jeff Shamma , Na Li

The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the…

Systems and Control · Electrical Eng. & Systems 2021-05-03 Taku Nonomura , Shunsuke Ono , Kumi Nakai , Yuji Saito

We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…

Optimization and Control · Mathematics 2023-11-06 Hoomaan Maskan , Konstantinos C. Zygalakis , Alp Yurtsever

This paper presents an inverse optimal control methodology and its application to training a predictive model of human motor control from a manipulation task. It introduces a convex formulation for learning both objective function and…

Systems and Control · Computer Science 2019-12-05 Marcel Menner , Peter Worsnop , Melanie N. Zeilinger

This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been…

Machine Learning · Computer Science 2020-03-04 Saurav Manchanda , Khoa Doan , Pranjul Yadav , S. Sathiya Keerthi

The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic…

Machine Learning · Statistics 2018-12-18 Martin Bompaire , Emmanuel Bacry , Stéphane Gaïffas

In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…

Machine Learning · Statistics 2018-10-16 Satoshi Hara , Takanori Maehara

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

Systems and Control · Computer Science 2016-08-09 Laurent Bako , Henrik Ohlsson

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…

Information Theory · Computer Science 2017-10-17 Oussama Dhifallah , Christos Thrampoulidis , Yue M. Lu

We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…

Optimization and Control · Mathematics 2020-10-06 Vignesh Sivaramakrishnan , Abraham P. Vinod , Meeko M. K. Oishi

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…

Machine Learning · Computer Science 2017-12-27 Xingguo Li , Raman Arora , Han Liu , Jarvis Haupt , Tuo Zhao

In many practical applications including remote sensing, multi-task learning, and multi-spectrum imaging, data are described as a set of matrices sharing a common column space. We consider the joint estimation of such matrices from their…

Statistics Theory · Mathematics 2023-06-07 Rakshith S Srinivasa , Seonho Kim , Kiryung Lee

We consider a class of stochastic optimal control problems with partial observation, and study their approximation by discrete-time control problems. We establish a convergence result by using weak convergence technique of Kushner and…

Optimization and Control · Mathematics 2023-05-22 Yunzhang Li , Xiaolu Tan , Shanjian Tang
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