Related papers: Violator Spaces: Structure and Algorithms
In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
Neutrino physics is one of the fundamental areas of research into the origins and properties of the Universe. Many experimental neutrino projects use sophisticated detectors to observe properties of these particles, and have turned to deep…
This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Motivated by $\ell_p$-optimization arising from sparse optimization, high dimensional data analytics and statistics, this paper studies sparse properties of a wide range of $p$-norm based optimization problems with $p > 1$, including…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
We develop a unified framework to characterize the power of higher-level algorithms for the constraint satisfaction problem (CSP), such as $k$-consistency, the Sherali-Adams LP hierarchy, and the affine IP hierarchy. As a result,…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
How to solve high-dimensional linear programs (LPs) efficiently is a fundamental question. Recently, there has been a surge of interest in reducing LP sizes using random projections, which can accelerate solving LPs independently of…
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…
We study a structured linear program (LP) that emerges in the need of ranking candidates or items in personalized recommender systems. Since the candidate set is only known in real time, the LP also needs to be formed and solved in real…
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two…