English
Related papers

Related papers: On Design of Polyhedral Estimates in Linear Invers…

200 papers

A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…

Information Theory · Computer Science 2016-01-26 Christos Thrampoulidis , Ehsan Abbasi , Babak Hassibi

In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…

Systems and Control · Computer Science 2013-12-02 Mathias Bürger , Giuseppe Notarstefano , Frank Allgöwer

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

Optimization and Control · Mathematics 2016-04-05 Patrick Holmes , Shreyas Kousik , Shankar Mohan , Ram Vasudevan

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…

Computational Geometry · Computer Science 2017-09-19 Siamak Yousefi , Xiao-Wen Chang , Henk Wymeersch , Benoit Champagne , Godfried Toussaint

The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…

Numerical Analysis · Mathematics 2019-01-28 Thomas Apel , Mariano Mateos , Johannes Pfefferer , Arnd Rösch

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…

Optimization and Control · Mathematics 2023-01-19 Arthur Marmin , Marc Castella , Jean-Christophe Pesquet , Laurent Duval

We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of…

Statistics Theory · Mathematics 2017-06-05 Dmitry Ostrovsky , Zaid Harchaoui , Anatoli Juditsky , Arkadi Nemirovski

Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…

Information Theory · Computer Science 2017-07-10 Jayant Apte , John MacLaren Walsh

Polyhedral Lyapunov functions can approximate any norm arbitrarily well. Because of this, they are used to study the stability of linear time varying and linear parameter varying systems without being conservative. However, the…

Optimization and Control · Mathematics 2021-03-08 Dimitris Kousoulidis , Fulvio Forni

Imprecise measurements of a point set P = (p1, ..., pn) can be modelled by a family of regions F = (R1, ..., Rn), where each imprecise region Ri contains a unique point pi. A retrieval models an accurate measurement by replacing an…

Computational Geometry · Computer Science 2025-12-09 Sarita de Berg , Ivor van der Hoog , Eva Rotenberg , Daniel Rutschmann , Sampson Wong

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…

Numerical Analysis · Mathematics 2025-08-12 Iulian Cîmpean , Andreea Grecu , Liviu Marin

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…

Machine Learning · Computer Science 2015-08-17 Dan Garber , Elad Hazan

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

Statistics Theory · Mathematics 2019-10-08 Zhengling Qi , Ying Cui , Yufeng Liu , Jong-Shi Pang

This paper considers a recoverable robust single-machine scheduling problem under polyhedral uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject…

Optimization and Control · Mathematics 2022-03-08 Matthew Bold , Marc Goerigk

This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…

Information Theory · Computer Science 2013-12-06 Samet Oymak , Christos Thrampoulidis , Babak Hassibi

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…

Optimization and Control · Mathematics 2022-11-29 Linchuan Wei , Alper Atamtürk , Andrés Gómez , Simge Küçükyavuz

In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse…

Optimization and Control · Mathematics 2024-04-08 Peijing Liu , Alper Atamtürk , Andrés Gómez , Simge Küçükyavuz

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…

Statistics Theory · Mathematics 2022-09-19 Xin Li , Dongya Wu

In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…

Statistics Theory · Mathematics 2022-01-24 Qiyang Han

We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing…

Information Theory · Computer Science 2015-05-27 Tomer Michaeli , Daniel Sigalov , Yonina C. Eldar