3 citations · 9 across the 9 of their papers we have counts for
14 papers
Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices
Johannes J. Brust, Jennifer B. Erway, Roummel F. Marcia
In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shap…
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…
A Dense Initialization for Limited-Memory Quasi-Newton Methods
Johannes Brust, Oleg Burdakov, Jennifer B. Erway +1
We consider a family of dense initializations for limited-memory quasi-Newton methods. The proposed initialization exploits an eigendecomposition-based separation of the full space…
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.…
Algorithm XXX: SC-SR1: Matlab software for solving shape-changing L-SR1 trust-region subproblems
Johannes Brust, Oleg Burdakov, Jennifer B. Erway +2
We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that solves trust-region. subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used i…
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 Solving L-SR1 Trust-Region Subproblems
Johannes Brust, Jennifer B. Erway, Roummel F. Marcia
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…
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…
Barrier methods for critical exponent problems in geometric analysis and mathematical physics
Jennifer Erway, Michael Holst
We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exp…