A dense initialization for limited-memory quasi-Newton methods

Johannes Brust (), Oleg Burdakov (), Jennifer B. Erway () and Roummel F. Marcia ()
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Johannes Brust: University of California Merced
Oleg Burdakov: Linköping University
Jennifer B. Erway: Wake Forest University
Roummel F. Marcia: University of California Merced

Computational Optimization and Applications, 2019, vol. 74, issue 1, No 5, 142 pages

Abstract: Abstract 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 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; 90C53; 90C06; 90C26; 65K05; 65K10; 65F10; 65F15 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-019-00112-x

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