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On Efficiently Comb...
On Efficiently Combining Limited Memory and Trust-Region Techniques
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- Burdakov, Oleg, 1953- (författare)
- Linköpings universitet,Optimeringslära,Tekniska högskolan
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- Gong, Lujin (författare)
- Samsung Advanced Institute of Technology, China Lab, Beijing, China
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- Yuan, Ya-Xiang (författare)
- State Key Laboratory of Scientic and Engineering Computing, Institute of Computational
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- Zikrin, Spartak (författare)
- Linköpings universitet,Optimeringslära,Tekniska högskolan
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(creator_code:org_t)
- Linköping : Linköping University Electronic Press, 2013
- Engelska 33 s.
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Serie: LiTH-MAT-R, 0348-2960 ; 2013:13
- Relaterad länk:
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficiently combine limited memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead compared with the cost of computing the quasi-Newton direction in line-search limited memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Unconstrained Optimization; Large-scale Problems; Limited Memory Methods
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