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Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
This note provides a novel, simple analysis of the method of conjugate gradients for the minimization of convex quadratic functions. In contrast with standard arguments, our proof is entirely self-contained and does not rely on the…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some…
In this paper, we consider the problem in defocus image deblurring. Previous classical methods follow two-steps approaches, i.e., first defocus map estimation and then the non-blind deblurring. In the era of deep learning, some researchers…
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more accurate physical analysis and understanding of experimental…
Federated Learning (FL) enables decentralized model training across multiple clients while optionally preserving data privacy. However, communication efficiency remains a critical bottleneck, particularly for large-scale models. In this…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
We present an analysis for the performance of decentralized consensus-based gradient (DCG) methods for solving optimization problems over a cluster network of nodes. This type of network is composed of a number of densely connected clusters…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…
We present SKA-SGD (Streaming Krylov-Accelerated Stochastic Gradient Descent), a novel optimization approach that accelerates convergence for ill-conditioned problems by projecting stochastic gradients onto a low-dimensional Krylov…
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents physical energy and the linear constraints enforce…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarised as minimising the residuum over a suitable Krylov subspace. It is shown that using the…
An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…