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Dense initializations for limited-memory quasi-Newton methods

Johannes Brust (jbrust***at***ucmerced.edu)
Oleg Burdakov (oleg.burdakov***at***liu.se)
Jennifer Erway (erwayjb***at***wfu.edu)
Roummel Marcia (rmarcia***at***ucmerced.edu)

Abstract: We consider a family of dense initializations for limited-memory quasi-Newton methods. The proposed initialization uses two parameters to approximate the curvature of the Hessian in two complementary subspaces. 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 of a shape-changing norm to define each subproblem. As with L-BFGS methods that traditionally use diagonal initialization, the dense initialization and the sequence of generated quasi-Newton matrices are never explicitly formed. Numerical experiments on the CUTEst test set suggest that this initialization together with the shape-changing trust-region method outperforms other L-BFGS methods for solving general nonconvex unconstrained optimization problems. While this dense initialization is proposed in the context of a special trust-region method, it has broad applications for more general quasi-Newton trust-region and line search methods. In fact, this initialization is suitable for use with any quasi-Newton update that admits a compact representation and, in particular, any member of the Broyden class of updates.

Keywords: Large-scale nonlinear optimization, limited-memory quasi-Newton methods, trust-region methods, quasi-Newton matrices, shape-changing norm

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Nonlinear Optimization (Other )

Citation: Technical Report 2017-1, Department of Mathematics and Statistics, Wake Forest University (2017).

Download: [PDF]

Entry Submitted: 10/06/2017
Entry Accepted: 10/06/2017
Entry Last Modified: 05/24/2018

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