Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/45243
DC Field | Value | Language |
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dc.contributor.author | Gratton, S. | - |
dc.contributor.author | Royer, C. W. | - |
dc.contributor.author | Vicente, Luís Nunes | - |
dc.date.accessioned | 2017-12-18T17:08:28Z | - |
dc.date.issued | 2016 | - |
dc.identifier.uri | https://hdl.handle.net/10316/45243 | - |
dc.description.abstract | Direct-search algorithms form one of the main classes of algorithms for smooth unconstrained derivative-free optimization, due to their simplicity and their well-established convergence results. They proceed by iteratively looking for improvement along some vectors or directions. In the presence of smoothness, first-order global convergence comes from the ability of the vectors to approximate the steepest descent direction, which can be quantified by a first-order criticality (cosine) measure. The use of a set of vectors with a positive cosine measure together with the imposition of a sufficient decrease condition to accept new iterates leads to a convergence result as well as a worst-case complexity bound. In this paper, we present a second-order study of a general class of direct-search methods. We start by proving a weak second-order convergence result related to a criticality measure defined along the directions used throughout the iterations. Extensions of this result to obtain a true second-order optimality one are discussed, one possibility being a method using approximate Hessian eigenvectors as directions (which is proved to be truly second-order globally convergent). Numerically guaranteeing such a convergence can be rather expensive to ensure, as it is indicated by the worst-case complexity analysis provided in this paper, but turns out to be appropriate for some pathological examples. | por |
dc.language.iso | eng | por |
dc.publisher | Taylor & Francis | por |
dc.relation | info:eu-repo/grantAgreement/FCT/5876/147205/PT | por |
dc.rights | embargoedAccess | - |
dc.title | A second-order globally convergent direct-search method and its worst-case complexity | por |
dc.type | article | - |
degois.publication.firstPage | 1105 | por |
degois.publication.lastPage | 1128 | por |
degois.publication.issue | 6 | por |
degois.publication.title | Optimization | por |
dc.relation.publisherversion | https://doi.org/10.1080/02331934.2015.1124271 | por |
dc.peerreviewed | yes | por |
dc.identifier.doi | 10.1080/02331934.2015.1124271 | - |
dc.identifier.doi | 10.1080/02331934.2015.1124271 | por |
degois.publication.volume | 65 | por |
dc.date.embargo | 2018-12-18T17:08:28Z | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.grantfulltext | open | - |
item.openairetype | article | - |
item.languageiso639-1 | en | - |
item.fulltext | Com Texto completo | - |
item.cerifentitytype | Publications | - |
crisitem.author.orcid | 0000-0002-5021-2357 | - |
crisitem.author.orcid | 0000-0003-1097-6384 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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File | Description | Size | Format | |
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DSdeterm2.pdf | 450.52 kB | Adobe PDF | View/Open |
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