Johannes Brust – Optimization Online

Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices

Published: 2022/09/24, Updated: 2022/10/09

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 “shape-changing” norm together with densely-initialized multipoint symmetric secant (MSS) matrices to approximate the Hessian. Shape-changing norms and dense initializations have been successfully used in the context of traditional quasi Newton … Read more

Compact Representations of Structured BFGS Matrices

Published: 2020/01/31, Updated: 2020/08/27

Nonlinear Optimization bfgs method, compact representation, large-scale optimization, limited memory method, quasi-newton methods

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. … Read more

A Dense initialization for limited-memory quasi-Newton methods

Published: 2017/10/06, Updated: 2019/05/23

Nonlinear Optimization, Unconstrained Optimization large scale nonlinear optimization, limited memory quasi-newton methods, quasi-newton matrices, shape-changing norm, trust-region methods

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 into two complementary subspaces, assigning a different initialization parameter to each subspace. This family of dense initializations is proposed in the context of a limited-memory Broyden- Fletcher-Goldfarb-Shanno (L-BFGS) trust-region method that makes use … Read more

ALGORITHM XXX: SC-SR1: MATLAB SOFTWARE FOR SOLVING SHAPE-CHANGING L-SR1 TRUST-REGION SUBPROBLEMS

Published: 2016/07/12, Updated: 2018/02/17

Unconstrained Optimization large-scale unconstrained optimization, limited memory quasi-newton methods, nonconvex optimization, shape-changing norm, symmetric rank-one update, trust-region methods

We present a MATLAB implementation of the shape-changing sym- metric rank-one (SC-SR1) method that solves trust-region subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix. The method takes advantage of two shape-changing norms [4, 3] to decompose the trust-region subproblem into two separate problems. Using one of … Read more

On Solving L-SR1 Trust-Region Subproblems

Published: 2015/06/18, Updated: 2016/08/12

Johannes Brust

Jennifer B. Erway

Roummel F. Marcia

Optimization Software and Modeling Systems, Unconstrained Optimization large-scale unconstrained optimization, limited memory quasi-newton methods, symmetric rank-one update, trust-region methods

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 representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the Sherman- … Read more