Related papers: Clarksons Algorithm for Violator Spaces

We investigate the space complexity of solving linear systems of equations. While all known deterministic or randomized algorithms solving a square system of $n$ linear equations in $n$ variables require $\Omega(\log^2 n)$ space, Ta-Shma…

Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…

Recursive estimates of large systems of equations in the context of least squares fitting is a common practice in different fields of study. For example, recursive adaptive filtering is extensively used in signal processing and control…

This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or…

An explicit algorithm for the minimization of an $\ell_1$ penalized least squares functional, with non-separable $\ell_1$ term, is proposed. Each step in the iterative algorithm requires four matrix vector multiplications and a single…

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…

We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe…

Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…

This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our…

While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…

We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions.…

Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…

This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods…

This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…

The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…