Related papers: Sparsity Preserving Algorithms for Octagons

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…

High-dimensional data has become ubiquitous across the sciences but presents computational and statistical challenges. A common approach to addressing these challenges is through sparsity. In this paper, we introduce a new concept of…

We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…

We investigate the methods that simultaneously enforce sparsity and low-rank structure in a matrix as often employed for sparse phase retrieval problems or phase calibration problems in compressive sensing. We propose a new approach for…

Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint…

This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…

For sparse matrices up to size $8 \times 8$, we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots chosen by a popular pivot selection strategy, so there is some…

Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…

In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…

The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…

The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…

In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…

A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…

Regression with sparse inputs is a common theme for large scale models. Optimizing the underlying linear algebra for sparse inputs allows such models to be estimated faster. At the same time, centering the inputs has benefits in improving…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…

We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…