相关论文: LSEMINK: A Modified Newton-Krylov Method for Log-S…

In this work, we propose an efficient two-metric adaptive projection method for solving the $\ell_1$-norm minimization problem. Our approach is inspired by the two-metric projection method, a simple yet elegant algorithm proposed by…

Support Vector Machines (SVMs) are among the most popular and the best performing classification algorithms. Various approaches have been proposed to reduce the high computation and memory cost when training and predicting based on…

We introduce a closed-form method for identification of discrete-time linear time-variant systems from data, formulating the learning problem as a regularized least squares problem where the regularizer favors smooth solutions within a…

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…

This paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…

Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…

The hybrid LSMR algorithm is proposed for large-scale general-form regularization. It is based on a Krylov subspace projection method where the matrix $A$ is first projected onto a subspace, typically a Krylov subspace, which is implemented…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

We present GenusSink, a new class of approximate generalized Sinkhorn algorithms with shortest-path-distance costs for bounded genus (e.g. planar) graphs, providing near-linear time: (1) pre-processing, (2) iteration step, (3) final…

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…

The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport (OT) and distributionally robust optimization (DRO). In…

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

This paper describes practical randomized algorithms for low-rank matrix approximation that accommodate any budget for the number of views of the matrix. The presented algorithms, which are aimed at being as pass efficient as needed, expand…