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A dense initializat...
A dense initialization for limited-memory quasi-Newton methods
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- Brust, Johannes (författare)
- University of California, Merced, CA, USA
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- Burdakov, Oleg, 1953- (författare)
- Linköpings universitet,Optimeringslära,Tekniska fakulteten
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- Erway, Jennifer B. (författare)
- Wake Forest University, Winston-Salem, NC, USA,Department of Mathematics
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- Marcia, Roummel F. (författare)
- University of California, Merced, CA, USA,Applied Mathematics
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(creator_code:org_t)
- 2019-05-29
- 2019
- Engelska.
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Ingår i: Computational Optimization and Applications. - : Springer. - 0926-6003 .- 1573-2894. ; 74:1, s. 121-142
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Abstract
Ämnesord
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- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Large-scale nonlinear optimization
- limited-memory quasi-Newton methods
- trust-region methods
- quasi-Newton matrices
- shape-changing norm.
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