Sökning: WFRF:(Burdakov Oleg 1953 ) >
On Efficiently Comb...
On Efficiently Combining Limited-Memory and Trust-Region Techniques
-
- Burdakov, Oleg, 1953- (författare)
- Linköpings universitet,Optimeringslära,Tekniska fakulteten
-
- Gong, Lujin (författare)
- Tencent, Beijing, China
-
- Zikrin, Spartak (författare)
- Linköpings universitet,Optimeringslära,Tekniska fakulteten
-
visa fler...
-
- Yuan, Ya-xiang (författare)
- State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing, China
-
visa färre...
-
(creator_code:org_t)
- 2016-06-27
- 2017
- Engelska.
-
Ingår i: Mathematical Programming Computation. - : Springer. - 1867-2949 .- 1867-2957. ; 9:1, s. 101-134
- Relaterad länk:
-
https://liu.diva-por... (primary) (Raw object)
-
visa fler...
-
http://liu.diva-port...
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
visa färre...
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 as 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
- Trust-Region Methods
- Shape-Changing Norm
- Eigenvalue Decomposition
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
Hitta via bibliotek
Till lärosätets databas