Related papers: Efficient Solution of Generalized Sylvester Equati…
We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to…
The convergence rates of iterative methods for solving a linear system $\mathbf{A} x = b$ typically depend on the condition number of the matrix $\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that…
The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
Two inverse-free iterative methods are developed for solving Sylvester matrix equations when the spectra of the coefficient matrices are on, or near, known disjoint subintervals of the real axis. Both methods use the recently-introduced…
Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of…
This paper provides a rigorous derivation and analysis of accelerated optimization algorithms through the lens of High-Resolution Ordinary Differential Equations (ODEs). While classical Nesterov acceleration is well-understood via…
We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, particularly when the degree of the…
It is well-known that a multilinear system with a nonsingular M-tensor and a positive right-hand side has a unique positive solution. Tensor splitting methods generalizing the classical iterative methods for linear systems have been…
Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Anderson mixing (AM) is a classical method that can accelerate fixed-point iterations by exploring historical information. Despite the successful application of AM in scientific computing, the theoretical properties of AM are still under…
Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…
When numerical solution of elliptic and parabolic partial differential equations is required to be highly accurate in space, the discrete problem usually takes the form of large-scale and sparse linear systems. In this work, as an…
This work is to provide a comprehensive treatment of the relationship between the theory of the generalized (palindromic) eigenvalue problem and the theory of the Sylvester-type equations. Under a regularity assumption for a specific matrix…
Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…
We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…
This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…
We present a convergence theory for Anderson acceleration (AA) applied to perturbed Newton methods (pNMs) for computing roots of nonlinear problems. Two important special cases are the classical Newton method and the Levenberg-Marquardt…
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…