Related papers: Optimal Diagonal Preconditioning

We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse…

The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…

When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…

The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…

We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…

We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…

High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…

The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We…

The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient…

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…

First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere…

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…

Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…

Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the…