3 citations · 9 across the 9 of their papers we have counts for
9 papers · 1 filter
A New Multipoint Symmetric Secant Method with a Dense Initial Matrix
Jennifer B. Erway, Mostafa Rezapour
In large-scale optimization, when either forming or storing Hessian matrices are prohibitively expensive, quasi-Newton methods are often used in lieu of Newton's method because the…
Trust-Region Algorithms for Training Responses: Machine Learning Methods Using Indefinite Hessian Approximations
Jennifer B. Erway, Joshua Griffin, Roummel F. Marcia +1
Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient d…
Compact representation of the full Broyden class of quasi-Newton updates
Omar DeGuchy, Jennifer B. Erway, Roummel F. Marcia
In this paper, we present the compact representation for matrices belonging to the the Broyden class of quasi-Newton updates, where each update may be either rank-one or rank-two.…
Trust-Region Methods for Sparse Relaxation
Lasith Adhikari, Jennifer B. Erway, Shelby Lockhart +1
In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and apply a limited-m…
On solving large-scale limited-memory quasi-Newton equations
Jennifer B. Erway, Roummel F. Marcia
We consider the problem of solving linear systems of equations arising with limited-memory members of the restricted Broyden class of updates and the symmetric rank-one (SR1) updat…
On efficiently computing the eigenvalues of limited-memory quasi-Newton matrices
Jennifer B. Erway, Roummel F. Marcia
In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce…
MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization
Jennifer B. Erway, Roummel F. Marcia
A MATLAB implementation of the More-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS ma…
Shifted L-BFGS Systems
Jennifer B. Erway, Vibhor Jain, Roummel F. Marcia
We investigate fast direct methods for solving systems of the form (B + G)x = y, where B is a limited-memory BFGS matrix and G is a symmetric positive-definite matrix. These system…
Limited-memory BFGS Systems with Diagonal Updates
Jennifer B. Erway, Roummel F. Marcia
In this paper, we investigate a formula to solve systems of the form (B + σI)x = y, where B is a limited-memory BFGS quasi-Newton matrix and σ is a positive constant. These types o…