Related papers: Inertial randomized Kaczmarz algorithms for solvin…
We study last-iterate convergence of SGD with greedy step size over smooth quadratics in the interpolation regime, a setting which captures the classical Randomized Kaczmarz algorithm as well as other popular iterative linear system…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
In this paper, we propose a novel adaptive stochastic extended iterative method, which can be viewed as an improved extension of the randomized extended Kaczmarz (REK) method, for finding the unique minimum Euclidean norm least-squares…
The randomized block Kaczmarz (RBK) method is a widely utilized iterative scheme for solving large-scale linear systems. However, the theoretical analysis and practical effectiveness of this method heavily rely on a good row paving of the…
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the…
We introduce a new iterative regularization method for solving inverse problems that can be written as systems of linear or non-linear equations in Hilbert spaces. The proposed averaged Kaczmarz (AVEK) method can be seen as a hybrid method…
Simple stochastic momentum methods are widely used in machine learning optimization, but their good practical performance is at odds with an absence of theoretical guarantees of acceleration in the literature. In this work, we aim to close…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…
Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their…
We present a numerically-stable parallel-in-time linear Kalman smoother. The smoother uses a novel highly-parallel QR factorization for a class of structured sparse matrices for state estimation, and an adaptation of the SelInv…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…