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In this paper, we show $O(1.415^n)$-time and $O(1.190^n)$-space exact algorithms for 0-1 integer programs where constraints are linear equalities and coefficients are arbitrary real numbers. Our algorithms are quadratically faster than…
The so-called \emph{simplified} Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of $k$ given sets, each set consisting of $n$ points, with the aim of minimizing the sum of…
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far…
Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
We propose a simple and effective method for designing approximation formulas for weighted analytic functions. We consider spaces of such functions according to weight functions expressing the decay properties of the functions. Then, we…
Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…
We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes…
We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
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 study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…