Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93316
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Yu, CKW | en_US |
dc.creator | Hu, Y | en_US |
dc.creator | Yang, X | en_US |
dc.creator | Choy, SK | en_US |
dc.date.accessioned | 2022-06-15T03:42:43Z | - |
dc.date.available | 2022-06-15T03:42:43Z | - |
dc.identifier.issn | 0233-1934 | en_US |
dc.identifier.uri | http://hdl.handle.net/10397/93316 | - |
dc.language.iso | en | en_US |
dc.publisher | Taylor & Francis | en_US |
dc.rights | © 2018 Informa UK Limited, trading as Taylor & Francis Group | en_US |
dc.rights | This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 26 Mar 2018 (published online), available at: http://www.tandfonline.com/10.1080/02331934.2018.1455831 | en_US |
dc.subject | Abstract convergence theorem | en_US |
dc.subject | Basic inequality | en_US |
dc.subject | Cobb–Douglas production efficiency problem | en_US |
dc.subject | Quasi-convex programming | en_US |
dc.subject | Subgradient method | en_US |
dc.title | Abstract convergence theorem for quasi-convex optimization problems with applications | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 1289 | en_US |
dc.identifier.epage | 1304 | en_US |
dc.identifier.volume | 68 | en_US |
dc.identifier.issue | 7 | en_US |
dc.identifier.doi | 10.1080/02331934.2018.1455831 | en_US |
dcterms.abstract | Quasi-convex optimization is fundamental to the modelling of many practical problems in various fields such as economics, finance and industrial organization. Subgradient methods are practical iterative algorithms for solving large-scale quasi-convex optimization problems. In the present paper, focusing on quasi-convex optimization, we develop an abstract convergence theorem for a class of sequences, which satisfy a general basic inequality, under some suitable assumptions on parameters. The convergence properties in both function values and distances of iterates from the optimal solution set are discussed. The abstract convergence theorem covers relevant results of many types of subgradient methods studied in the literature, for either convex or quasi-convex optimization. Furthermore, we propose a new subgradient method, in which a perturbation of the successive direction is employed at each iteration. As an application of the abstract convergence theorem, we obtain the convergence results of the proposed subgradient method under the assumption of the Hölder condition of order p and by using the constant, diminishing or dynamic stepsize rules, respectively. A preliminary numerical study shows that the proposed method outperforms the standard, stochastic and primal-dual subgradient methods in solving the Cobb–Douglas production efficiency problem. | en_US |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | Optimization, 2019, v. 68, no. 7, p. 1289-1304 | en_US |
dcterms.isPartOf | Optimization | en_US |
dcterms.issued | 2019 | - |
dc.identifier.scopus | 2-s2.0-85044441978 | - |
dc.identifier.eissn | 1029-4945 | en_US |
dc.description.validate | 202206 bcfc | en_US |
dc.description.oa | Accepted Manuscript | en_US |
dc.identifier.FolderNumber | AMA-0393 | - |
dc.description.fundingSource | RGC | en_US |
dc.description.fundingSource | Others | en_US |
dc.description.fundingText | PolyU | en_US |
dc.description.pubStatus | Published | en_US |
dc.identifier.OPUS | 6830456 | - |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Yang_Abstract_Convergence_Theorem.pdf | Pre-Published version | 726.15 kB | Adobe PDF | View/Open |
Page views
57
Last Week
0
0
Last month
Citations as of May 19, 2024
Downloads
61
Citations as of May 19, 2024
SCOPUSTM
Citations
8
Citations as of May 16, 2024
WEB OF SCIENCETM
Citations
6
Citations as of May 16, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.