相关论文: On solving large-scale limited-memory quasi-Newton…

In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…

Exemplar-based class-incremental learning is to recognize new classes while not forgetting old ones, whose samples can only be saved in limited memory. The ratio fluctuation of new samples to old exemplars, which is caused by the variation…

In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is…

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…

In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

In this paper, we investigate a formula to solve systems of the form (B + {\sigma}I)x = y, where B is a limited-memory BFGS quasi-Newton matrix and {\sigma} is a positive constant. These types of systems arise naturally in large-scale…

We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…

The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…

This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates…

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…

In this work we introduce and study novel Quasi Newton minimization methods based on a Hessian approximation Broyden Class-\textit{type} updating scheme, where a suitable matrix $\tilde{B}_k$ is updated instead of the current Hessian…

Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…

In this work we describe an Adaptive Regularization using Cubics (ARC) method for large-scale nonconvex unconstrained optimization using Limited-memory Quasi-Newton (LQN) matrices. ARC methods are a relatively new family of optimization…

In this brief, we improve the Broad Learning System (BLS) [7] by reducing the computational complexity of the incremental learning for added inputs. We utilize the inverse of a sum of matrices in [8] to improve a step in the pseudoinverse…

In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory,…