Publications related to An Adaptive Least-squares Algorithm for the Elliptic Monge-ampere Equation

Related publications (13)

Phase Diagram of Compressed Sensing with l0-norm Regularization

Lenka Zdeborová, Florent Gérard Krzakala, Damien Yves Valery Barbier

Noiseless compressive sensing is a two-step setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on l(1) regularization, provides an efficient and robust way to address thi ...

IOP Publishing Ltd2025

Theory and applications of the sum-of-squares technique

Luca Pesce, Giovanni Piccioli, Elisabetta Cornacchia

The sum-of-squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method t ...

2024

The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques

Guillaume Anciaux, Simone Deparis, Yannis Dirk Voet

The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, ...

PERGAMON-ELSEVIER SCIENCE LTD2022

Regularized economic model predictive control with barrier functions

Colin Neil Jones, Altug Bitlislioglu

In this article, we consider the use of barrier functions as a regularizing cost in economic model predictive control (EMPC). We focus on a specific variant, EMPC with generalized terminal constraints (G-EMPC), as it is suitable for tackling large-scale pr ...

WILEY2020

Learning Non-Parametric Models with Guarantees: A Smooth Lipschitz Regression Approach

Colin Neil Jones, Emilio Maddalena

We propose a non-parametric regression methodology that enforces the regressor to be fully consistent with the sample set and the ground-truth regularity assumptions. As opposed to the Nonlinear Set Membership technique, this constraint guarantees the atta ...

ELSEVIER2020

Generalized maximum entropy estimation

John Lygeros, Peyman Mohajerin Esfahani, Tobias Sutter

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme ...

2019

Efficient Variance-Reduced Learning Over Multi-Agent Networks

Ali H. Sayed, Kun Yuan, Bicheng Ying

This work develops a fully decentralized variance-reduced learning algorithm for multi-agent networks where nodes store and process the data locally and are only allowed to communicate with their immediate neighbors. In the proposed algorithm, there is no ...

IEEE COMPUTER SOC2018

Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

Linda Maria De Cave

Given a planar domain Omega, we study the Dirichlet problem {-divA(x, del v) = f in Omega, v = 0 on partial derivative Omega, where the higher-order term is a quasilinear elliptic operator, and f belongs to the Zygmund space L(log L)delta(log log log L)(be ...

2016

Robust Principal Component Analysis on Graphs

Pierre Vandergheynst, Xavier Bresson, Michael Bronstein, Vasilis Kalofolias, Nauman Shahid

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first iss ...

2015

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Daniel Kressner, André Uschmajew, Michael Maximilian Steinlechner

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...

Siam Publications2014

Fast Variational Bayesian Inference for Non-Conjugate Matrix Factorization Models

Matthias Seeger

Probabilistic matrix factorization methods aim to extract meaningful correlation structure from an incomplete data matrix by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to such l ...

2012

Efficient Image Reconstruction Under Sparsity Constraints With Application To Mri And Bioluminescence Tomography

Michaël Unser, Matthieu Guerquin-Kern, Jean-Charles Baritaux

Most bioimaging modalities rely on indirect measurements of the quantity under investigation. The image is obtained as the result of an optimization problem involving a physical model of the measurement system. Due to the ill-posedness of the above problem ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Spline-Based Image-to-Volume Registration for Three-Dimensional Electron Microscopy

Michaël Unser, Philippe Thévenaz

This paper presents an algorithm based on a continuous framework for a posteriori angular and translational assignment in three-dimensional electron microscopy (3DEM) of single particles. Our algorithm can be used advantageously to refine the assignment of ...

Elsevier2005