Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions

We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiabl...

Full description

Saved in:
Bibliographic Details
Published in:Vietnam journal of mathematics 2020-06, Vol.48 (2), p.391-406
Main Authors: Volle, M., Martínez-Legaz, J. E.
Format: Article
Language:English
Subjects:
Domains
Mathematics
Mathematics and Statistics
Optimization and Control
Original Article
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893
cites cdi_FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893
container_end_page 406
container_issue 2
container_start_page 391
container_title Vietnam journal of mathematics
container_volume 48
creator Volle, M.
Martínez-Legaz, J. E.
description We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiable on the relative interior of this effective domain. We give an application to surrogate duality in quasiconvex programming.
doi_str_mv 10.1007/s10013-020-00391-6
format article
fullrecord <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_03438166v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2412164154</sourcerecordid><originalsourceid>FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893</originalsourceid><addsrcrecordid>eNp9kE1OwzAQhSMEEqVwAVaRWLEIzNiJmyyrClqkSvy0SOwsJ7WL2zQudlLRHXfghpwEl6CyYzMzGn3vaeYFwTnCFQL0rp2vSCMgEAHQDCN2EHQIhSQihKSH-xlfjoMT5xYAwFLW6wTTiVnJ8EmuhF260FTh0EpZ5dLOvz4-H7S0binKUoSTJp9ppaSVVa1Frktdb0OjwsdGOF2YaiPfw9umKmptKncaHClROnn227vB8-3NdDCKxvfDu0F_HBU0oXVEC0JiCjmDGaBQKWFCKSGKhFBkszRHikmqMoFpHOcKZkXCPMKyLJcFijSj3eCy9X0VJV9b7Z_YciM0H_XHfLcDGtMUGdugZy9adm3NWyNdzRemsZU_j5MYCbIYk9hTpKUKa5yzUu1tEfguad4mzX3S_CdpzryItiLn4Wou7Z_1P6pvTOGBWw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2412164154</pqid></control><display><type>article</type><title>Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions</title><source>Springer Nature</source><creator>Volle, M. ; Martínez-Legaz, J. E.</creator><creatorcontrib>Volle, M. ; Martínez-Legaz, J. E.</creatorcontrib><description>We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiable on the relative interior of this effective domain. We give an application to surrogate duality in quasiconvex programming.</description><identifier>ISSN: 2305-221X</identifier><identifier>EISSN: 2305-2228</identifier><identifier>DOI: 10.1007/s10013-020-00391-6</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Domains ; Mathematics ; Mathematics and Statistics ; Optimization and Control ; Original Article</subject><ispartof>Vietnam journal of mathematics, 2020-06, Vol.48 (2), p.391-406</ispartof><rights>Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2020</rights><rights>Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2020.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893</citedby><cites>FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893</cites><orcidid>0000-0002-6845-6202</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://univ-avignon.hal.science/hal-03438166$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Volle, M.</creatorcontrib><creatorcontrib>Martínez-Legaz, J. E.</creatorcontrib><title>Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions</title><title>Vietnam journal of mathematics</title><addtitle>Vietnam J. Math</addtitle><description>We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiable on the relative interior of this effective domain. We give an application to surrogate duality in quasiconvex programming.</description><subject>Domains</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Optimization and Control</subject><subject>Original Article</subject><issn>2305-221X</issn><issn>2305-2228</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhSMEEqVwAVaRWLEIzNiJmyyrClqkSvy0SOwsJ7WL2zQudlLRHXfghpwEl6CyYzMzGn3vaeYFwTnCFQL0rp2vSCMgEAHQDCN2EHQIhSQihKSH-xlfjoMT5xYAwFLW6wTTiVnJ8EmuhF260FTh0EpZ5dLOvz4-H7S0binKUoSTJp9ppaSVVa1Frktdb0OjwsdGOF2YaiPfw9umKmptKncaHClROnn227vB8-3NdDCKxvfDu0F_HBU0oXVEC0JiCjmDGaBQKWFCKSGKhFBkszRHikmqMoFpHOcKZkXCPMKyLJcFijSj3eCy9X0VJV9b7Z_YciM0H_XHfLcDGtMUGdugZy9adm3NWyNdzRemsZU_j5MYCbIYk9hTpKUKa5yzUu1tEfguad4mzX3S_CdpzryItiLn4Wou7Z_1P6pvTOGBWw</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Volle, M.</creator><creator>Martínez-Legaz, J. E.</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-6845-6202</orcidid></search><sort><creationdate>20200601</creationdate><title>Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions</title><author>Volle, M. ; Martínez-Legaz, J. E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Domains</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Optimization and Control</topic><topic>Original Article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Volle, M.</creatorcontrib><creatorcontrib>Martínez-Legaz, J. E.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Vietnam journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Volle, M.</au><au>Martínez-Legaz, J. E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions</atitle><jtitle>Vietnam journal of mathematics</jtitle><stitle>Vietnam J. Math</stitle><date>2020-06-01</date><risdate>2020</risdate><volume>48</volume><issue>2</issue><spage>391</spage><epage>406</epage><pages>391-406</pages><issn>2305-221X</issn><eissn>2305-2228</eissn><abstract>We observe that a quasiconvex function which is evenly quasiconvex at a point is not necessarily Greenberg–Pierskalla (briefly, G-P) subdifferentiable at that point, but we prove that a quasiconvex function which is upper semicontinuous on the segments of its effective domain is G-P subdifferentiable on the relative interior of this effective domain. We give an application to surrogate duality in quasiconvex programming.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s10013-020-00391-6</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-6845-6202</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 2305-221X
ispartof Vietnam journal of mathematics, 2020-06, Vol.48 (2), p.391-406
issn 2305-221X
2305-2228
language eng
recordid cdi_hal_primary_oai_HAL_hal_03438166v1
source Springer Nature
subjects Domains
Mathematics
Mathematics and Statistics
Optimization and Control
Original Article
title Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T18%3A59%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Some%20Remarks%20on%20Greenberg%E2%80%93Pierskalla%20Subdifferentiability%20of%20Quasiconvex%20Functions&rft.jtitle=Vietnam%20journal%20of%20mathematics&rft.au=Volle,%20M.&rft.date=2020-06-01&rft.volume=48&rft.issue=2&rft.spage=391&rft.epage=406&rft.pages=391-406&rft.issn=2305-221X&rft.eissn=2305-2228&rft_id=info:doi/10.1007/s10013-020-00391-6&rft_dat=%3Cproquest_hal_p%3E2412164154%3C/proquest_hal_p%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c353t-3c22430b60d01af826affaac52316d8b13158f9a1844bf0dc5626a699bec1a893%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2412164154&rft_id=info:pmid/&rfr_iscdi=true