Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/45237
DC Field | Value | Language |
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dc.contributor.author | Dodangeh, Mahdi | - |
dc.contributor.author | Vicente, Luís Nunes | - |
dc.contributor.author | Zhang, Zaikun | - |
dc.date.accessioned | 2017-12-18T16:32:39Z | - |
dc.date.issued | 2016 | - |
dc.identifier.uri | https://hdl.handle.net/10316/45237 | - |
dc.description.abstract | The worst case complexity of direct-search methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. For smooth unconstrained optimization, it is now known that such methods require at most \mathcal {O}(n^2\epsilon ^{-2}) function evaluations to compute a gradient of norm below \epsilon \in (0,1), where n is the dimension of the problem. Such a maximal effort is reduced to \mathcal {O}(n^2\epsilon ^{-1}) if the function is convex. The factor n^2 has been derived using the positive spanning set formed by the coordinate vectors and their negatives at all iterations. In this paper, we prove that such a factor of n^2 is optimal in these worst case complexity bounds, in the sense that no other positive spanning set will yield a better order of n. The proof is based on an observation that reveals the connection between cosine measure in positive spanning and sphere covering. | por |
dc.language.iso | eng | por |
dc.publisher | Springer Berlin Heidelberg | por |
dc.relation | info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT | por |
dc.rights | embargoedAccess | - |
dc.title | On the optimal order of worst case complexity of direct search | por |
dc.type | article | - |
degois.publication.firstPage | 699 | por |
degois.publication.lastPage | 708 | por |
degois.publication.issue | 4 | por |
degois.publication.title | Optimization Letters | por |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s11590-015-0908-1 | por |
dc.peerreviewed | yes | por |
dc.identifier.doi | 10.1007/s11590-015-0908-1 | por |
dc.identifier.doi | 10.1007/s11590-015-0908-1 | - |
degois.publication.volume | 10 | por |
dc.date.embargo | 2018-12-18T16:32:39Z | - |
item.fulltext | Com Texto completo | - |
item.grantfulltext | open | - |
item.languageiso639-1 | en | - |
item.cerifentitytype | Publications | - |
item.openairetype | article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
crisitem.author.orcid | 0000-0003-1097-6384 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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