compact representation – Optimization Online

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

On solving large-scale limited-memory quasi-Newton equations

Published: 2015/10/21, Updated: 2016/01/17

Jennifer B. Erway

Roummel F. Marcia

Nonlinear Optimization broyden-fletcher-goldfarb-shanno update, compact representation, davidon-fletcher-powell update, limited memory quasi-newton methods, restricted broyden class of updates, sherman-morrison-woodbury formula, symmetric rank-one update

We consider the problem of solving linear systems of equations with limited- memory members of the restricted Broyden class and symmetric rank-one matrices. In this paper, we present various methods for solving these linear systems, and propose a new approach based on a practical implementation of the compact representation for the inverse of these limited-memory … Read more