Related papers: Convergence of the Conjugate Gradient Method on Si…

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…

The focus of this paper is on the analysis of the Conjugate Gradient method applied to a non-symmetric system of linear equations, arising from a Fast Fourier Transform-based homogenization method due to (Moulinec and Suquet, 1994).…

We consider the problem of solving linear least squares problems in a framework where only evaluations of the linear map are possible. We derive randomized methods that do not need any other matrix operations than forward evaluations,…

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

We consider estimators obtained by iterates of the conjugate gradient (CG) algorithm applied to the normal equation of prototypical statistical inverse problems. Stopping the CG algorithm early induces regularisation, and optimal…

The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…

Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…

We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of…

Alternating least squares (ALS) is often considered the workhorse algorithm for computing the rank-R canonical tensor approximation, but for certain problems its convergence can be very slow. The nonlinear conjugate gradient (NCG) method…

In this paper, we propose a subgradient algorithm with a non-asymptotic convergence guarantee to solve copositive programming problems. The subproblem to be solved at each iteration is a standard quadratic programming problem, which is…

We study deterministic matrix completion problem, i.e., recovering a low-rank matrix from a few observed entries where the sampling set is chosen as the edge set of a Ramanujan graph. We first investigate projected gradient descent (PGD)…

This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…

SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent…

We study the convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions (where the sum is strongly convex) and a non-smooth convex function. At each…

Factorization-based gradient descent is a scalable and efficient algorithm for solving low-rank matrix completion. Recent progress in structured non-convex optimization has offered global convergence guarantees for gradient descent under…