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Dense Initializations for Limited-Memory Quasi-Newton Methods
University of California, Merced, CA, USA.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .ORCID iD: 0000-0003-1836-4200
Wake Forest University, Winston-Salem, NC, USA. (Department of Mathematics)
University of California, Merced, CA, USA. (Applied Mathematics)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword [en]
Large-scale nonlinear optimization, limited-memory quasi-Newton methods, trust-region methods, quasi-Newton matrices, shape-changing norm.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-143315OAI: oai:DiVA.org:liu-143315DiVA: diva2:1162458
Available from: 2017-12-04 Created: 2017-12-04 Last updated: 2017-12-04

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https://arxiv.org/abs/1710.02396

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