| Title:
|
Recursive form of general limited memory variable metric methods (English) |
| Author:
|
Lukšan, Ladislav |
| Author:
|
Vlček, Jan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
224-235 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately $4 m n$ multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm 1, proposed in this report, confirm its practical efficiency. (English) |
| Keyword:
|
unconstrained optimization |
| Keyword:
|
large scale optimization |
| Keyword:
|
limited memory methods |
| Keyword:
|
variable metric updates |
| Keyword:
|
recursive matrix formulation |
| Keyword:
|
algorithms |
| MSC:
|
49K35 |
| MSC:
|
49M30 |
| MSC:
|
90C06 |
| MSC:
|
90C26 |
| MSC:
|
90C47 |
| MSC:
|
90C51 |
| MSC:
|
90C53 |
| idZBL:
|
Zbl 1266.49060 |
| idMR:
|
MR3085394 |
| . |
| Date available:
|
2013-07-22T08:44:51Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143365 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[12] Vlček, J., Lukšan, L.: Generalizations of the Limited-memory BFGS Method Based on Quasi-product Form of Update..Report V-1060, Institute of Computer Science AS CR, Prague 2009. |
| . |
