Constraint Qualifications for Vector Optimization Problems in Real Topological Spaces

In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affine...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Axioms Ročník 12; číslo 8; s. 783
Hlavní autor:	Zeng, Renying
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel MDPI AG 01.08.2023
Témata:	affine functions constraint qualifications convex functions Duality theorem generalized affine functions generalized convex functions Graphs Mathematical optimization Mathematical research Optimization real linear topological spaces Topological spaces Topology Canada
ISSN:	2075-1680, 2075-1680
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constraints, and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.
AbstractList	In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constraints, and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.
Audience	Academic
Author	Zeng, Renying
Author_xml	– sequence: 1 givenname: Renying orcidid: 0000-0001-9073-9981 surname: Zeng fullname: Zeng, Renying
BookMark	eNp1kctr3DAQxk1IIWmaa86GnjfVy7J0DEsfgUDSNslVjOTRosW2XEkLTf_6KruhL6h0GPFpfh_DfK-b4znO2DQXlFxyrsk7-B7ilCkjivSKHzWnjPTdikpFjv94nzTnOW9JPZpyRflp87COcy4JwlzazzsYgw8OSqhi62NqH9GVWm6XEqbwY__R3qVoR5xyG-b2C8LY3scljnFTwbH9uoDD_KZ55WHMeP5Sz5qHD-_v159WN7cfr9dXNysnKCsrqqHTnafAle3sQCgwST32QgwOQCKzFqVUYuiU6FF2HjmxhAgi0VIngJ811wffIcLWLClMkJ5MhGD2QkwbA6kEN6LxpBOScT-gtkIob63SxAsqNWjkVFevtwevJcVvO8zFbOMuzXV8w1Qne6mFYLXr8tC1gWoaZh_r8ly9A07B1Ux8qPpVL5lQhDH5G3Ap5pzQ_xqTEvMcnfk7ugqIfwAXyn7zzzGN_8N-AuJ5oGE
CitedBy_id	crossref_primary_10_1515_math_2024_0073
Cites_doi	10.1007/s10957-006-9140-6 10.1080/02331934.2020.1847109 10.1080/02331938508843061 10.1007/BFb0120929 10.1073/pnas.39.1.42 10.1007/BF02191762 10.1016/j.na.2010.04.020 10.1016/j.jmaa.2008.10.009 10.1007/978-3-642-02431-3 10.1080/0233193021000031615 10.1006/jmaa.1997.5568 10.1287/moor.22.4.977 10.1007/978-3-642-21114-0 10.1007/978-3-662-00547-7 10.1287/moor.9.1.87 10.1007/978-3-642-50280-4 10.1137/0712056
ContentType	Journal Article
Copyright	COPYRIGHT 2023 MDPI AG 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml	– notice: COPYRIGHT 2023 MDPI AG – notice: 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID	AAYXX CITATION 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PTHSS Q9U DOA
DOI	10.3390/axioms12080783
DatabaseName	CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Korea Engineering Research Database ProQuest Central Student SciTech Collection (ProQuest) ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition Engineering Collection ProQuest Central Basic DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni)
DatabaseTitleList	CrossRef Publicly Available Content Database
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: ProQuest Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EISSN	2075-1680
ExternalDocumentID	oai_doaj_org_article_f054623fde9b448fbb890f4169a9e319 A762480226 10_3390_axioms12080783
GeographicLocations	Canada
GeographicLocations_xml	– name: Canada
GroupedDBID	5VS 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ABUWG ACUHS ADBBV AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS AMVHM ARAPS AZQEC BCNDV BENPR BGLVJ BPHCQ CCPQU CITATION DWQXO EAD EAP ESX GNUQQ GROUPED_DOAJ HCIFZ IAO ITC K6V K7- KQ8 L6V M7S MODMG M~E OK1 PHGZM PHGZT PIMPY PQGLB PQQKQ PROAC PTHSS QF4 QN7 3V. 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D M0N P62 PKEHL PQEST PQUKI Q9U
ID	FETCH-LOGICAL-c412t-19a595f1a38b5bd01a261fe744dcaa6e2bbe6684d5847e65fe30b00406eb1c4a3
IEDL.DBID	M7S
ISICitedReferencesCount	2
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001056272400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2075-1680
IngestDate	Fri Oct 03 12:46:19 EDT 2025 Fri Jul 25 11:59:50 EDT 2025 Tue Nov 04 18:28:33 EST 2025 Tue Nov 18 20:56:28 EST 2025 Sat Nov 29 07:17:46 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	8
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c412t-19a595f1a38b5bd01a261fe744dcaa6e2bbe6684d5847e65fe30b00406eb1c4a3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0001-9073-9981
OpenAccessLink	https://www.proquest.com/docview/2856769442?pq-origsite=%requestingapplication%
PQID	2856769442
PQPubID	2032429
ParticipantIDs	doaj_primary_oai_doaj_org_article_f054623fde9b448fbb890f4169a9e319 proquest_journals_2856769442 gale_infotracacademiconefile_A762480226 crossref_primary_10_3390_axioms12080783 crossref_citationtrail_10_3390_axioms12080783
PublicationCentury	2000
PublicationDate	2023-08-01
PublicationDateYYYYMMDD	2023-08-01
PublicationDate_xml	– month: 08 year: 2023 text: 2023-08-01 day: 01
PublicationDecade	2020
PublicationPlace	Basel
PublicationPlace_xml	– name: Basel
PublicationTitle	Axioms
PublicationYear	2023
Publisher	MDPI AG
Publisher_xml	– name: MDPI AG
References	Jeyakumar (ref_3) 1985; 16 Zhao (ref_18) 2016; 17 ref_13 Zeng (ref_6) 2006; 131 Kanzi (ref_17) 2009; 351 Zeng (ref_5) 2002; 51 ref_20 ref_1 Robinson (ref_12) 1981; 14 Fang (ref_14) 2010; 73 Robinson (ref_11) 1975; 12 Li (ref_7) 1997; 215 ref_16 Khazayel (ref_19) 2022; 71 ref_15 Ye (ref_8) 1997; 22 ref_9 Aubin (ref_10) 1984; 9 Fan (ref_2) 1953; 39 Li (ref_4) 1994; 1
References_xml	– volume: 131 start-page: 281 year: 2006 ident: ref_6 article-title: Generalized Motzkin Theorem of the Alternative and Vector Optimization Problems publication-title: J. Optim. Theo. Appl. doi: 10.1007/s10957-006-9140-6 – volume: 71 start-page: 2033 year: 2022 ident: ref_19 article-title: On the Optimality Conditions for DC Vector Optimization Problems publication-title: Optimization doi: 10.1080/02331934.2020.1847109 – volume: 16 start-page: 643 year: 1985 ident: ref_3 article-title: Convexlike Alternative Theorems and Mathematical Programming publication-title: Optimization doi: 10.1080/02331938508843061 – volume: 14 start-page: 206 year: 1981 ident: ref_12 article-title: Some Continuity Properties of Polyhedral Multifunctions publication-title: Math. Program. Stud. doi: 10.1007/BFb0120929 – volume: 39 start-page: 42 year: 1953 ident: ref_2 article-title: Minimax Theorems publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.39.1.42 – volume: 1 start-page: 63 year: 1994 ident: ref_4 article-title: Lagrange Multipliers and Saddle Points in Multiobjective Programming publication-title: J. Optim. Theo. Appl. doi: 10.1007/BF02191762 – volume: 73 start-page: 1143 year: 2010 ident: ref_14 article-title: Constraint Qualifications for Optimality Conditions and Total Lagrange Dualities in Convex Infinite Programming publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.04.020 – volume: 351 start-page: 170 year: 2009 ident: ref_17 article-title: Nonsmooth Semi-Infinite Programming Problems with Mixed Constraints publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.10.009 – ident: ref_16 – ident: ref_9 doi: 10.1007/978-3-642-02431-3 – volume: 51 start-page: 709 year: 2002 ident: ref_5 article-title: Generalized Gordan Alternative Theorem with Weakened Convexity and its Applications publication-title: Optimization doi: 10.1080/0233193021000031615 – ident: ref_13 – volume: 215 start-page: 297 year: 1997 ident: ref_7 article-title: Lagrangian Multipliers, Saddle Points and Duality in Vector Optimization of Set-Valued Maps publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1997.5568 – volume: 22 start-page: 977 year: 1997 ident: ref_8 article-title: Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constriants publication-title: Math. Oper. Res. doi: 10.1287/moor.22.4.977 – volume: 17 start-page: 879 year: 2016 ident: ref_18 article-title: Constraint Qualification for Quasiconvex Inequality System with Applications in Constraint Optimization publication-title: J. Nonlinear Convex. Anal. – ident: ref_20 doi: 10.1007/978-3-642-21114-0 – ident: ref_1 doi: 10.1007/978-3-662-00547-7 – volume: 9 start-page: 87 year: 1984 ident: ref_10 article-title: Lipschitz Behavior of Solutions to Convex Minimization Problems publication-title: Math. Oper. Res. doi: 10.1287/moor.9.1.87 – ident: ref_15 doi: 10.1007/978-3-642-50280-4 – volume: 12 start-page: 754 year: 1975 ident: ref_11 article-title: Stability Theory for Systems of Inequalities. Part I: Linear Systems publication-title: SIAM J. Numer. Anal. doi: 10.1137/0712056
SSID	ssj0000913813
Score	2.248599
Snippet	In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our...
SourceID	doaj proquest gale crossref
SourceType	Open Website Aggregation Database Enrichment Source Index Database
StartPage	783
SubjectTerms	affine functions constraint qualifications convex functions Duality theorem generalized affine functions generalized convex functions Graphs Mathematical optimization Mathematical research Optimization real linear topological spaces Topological spaces Topology
SummonAdditionalLinks	– databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA5SPOhBfGK1Sg6Cp8XdJPvIUcXixVp80VtIsgkUtC1uFX--M8m26KF48boEkkwm88jOfB8hZxlirJXWJ3le1Ql4qDqpshJ0mWurC2uY1ZFsohwMqtFIDn9QfWFNWIQHjoK78BBTgIv2tZMGUglvTCVTD2GE1NLxAPjJ0lL-SKaCDZYZuCIeURo55PUX-ms8fWsyliLAOv_lhQJY_yqTHPxMf5tstQEivYwL2yFrbrJLNu-W6KrNHnlGls3A7TCnAQPDLx7eKISg9CU8xNN7MAZvbZclHUbemIaOJ_QBYkP6FMkR8Ijo4wzrsvbJc__m6fo2aekREisyNk8yqXOZ-0zzyuSmTjMN2ZB3pRC11bpwzBhXFJWo8U-oK3LveBoubQH22QrND0hnMp24Q0K99akV3tsc4cZYqRnIFiYxnhvBXNolyUJcyrbY4bjNVwU5BIpX_RZvl5wvx88iasbKkVco_eUoRLsOH0AHVKsD6i8dgOnw7BTeSViW1W1rAWwO0a3UJVh8gT3FRZf0Fser2svaKFblWOgrBDv6j9Uckw3kpI9Vgj3Smb9_uBOybj_n4-b9NOjpN8Yh7gk priority: 102 providerName: Directory of Open Access Journals
Title	Constraint Qualifications for Vector Optimization Problems in Real Topological Spaces
URI	https://www.proquest.com/docview/2856769442 https://doaj.org/article/f054623fde9b448fbb890f4169a9e319
Volume	12
WOSCitedRecordID	wos001056272400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: DOA dateStart: 20120101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources (selected full-text only) customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: M~E dateStart: 20120101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: K7- dateStart: 20120301 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: M7S dateStart: 20120301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: BENPR dateStart: 20120301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Publicly Available Content Database customDbUrl: eissn: 2075-1680 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000913813 issn: 2075-1680 databaseCode: PIMPY dateStart: 20120301 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LbxMxEB5By4EeeCMCJfIBiZPVtdf7OqEWpQKhhlUfqJws22ujSDRJswFx4rcz43WCeigXLj7sWlp7x_PwePx9AG8EYaxVLvCiqDuOHqrjtahwLefGmdJZ6cxANlFNp_XlZdOmhFufyio3NjEa6m7hKEd-IOuCqjGVku-W15xYo-h0NVFo3IVdQkkQsXTvbJtjIczLWuQDVmOOu_sD82u2uOqFzAhmPb_hiyJk_22GOXqb44f_O85H8CDFmexwWBiP4Y6fP4G9ky1Ia_8ULoisM1JErFmE0gib_B3DSJZ9ifl89hltylW6rMnagX6mZ7M5O8UQk50PHAskaXa2pPKuZ3BxPDl__4EnlgXulJBrLhpTNEUQJq9tYbtMGNxUBV8p1TljSi-t9WVZq44OVH1ZBJ9nUfdLNPNOmfw57MwXc_8CWHAhcyoEVxBqmayMbDx6SWlDbpX02Qj45n9rlyDIaZrfNW5FSD76pnxG8HbbfzmAb9za84jEt-1FoNnxwWL1TScd1AHDU4z2Qucbi7vSYG3dZAEj0sbgOEWDnyPha1JtHJYz6YYCTo5AsvQhOg5FV5PLEexvhK-Tzvf6r-Rf_vv1K7hPpPVDGeE-7KxXP_xruOd-rmf9agy7R5NpezqO2QFsP1V8HJc1tb8n-L79eNJ-_QNvyAKy
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VggQceKMuFPABxClqYjsPHxAqj6rVtksFW9Sbazs2WqndXTbL60_xG5lxkkU9lFsPXBMriePPM2N75vsAnmfEsVa6kOR5VSfooeqkykrEsjDOFM5yZ1qxiXI0qo6P1eEa_O5rYSitsreJ0VDXM0d75Fu8yikbU0r-ev41IdUoOl3tJTRaWAz9rx-4ZGte7b3D8X3B-c778dvdpFMVSJzM-DLJlMlVHjIjKpvbOs0MLiKCL6WsnTGF59b6oqhkTQeIvsiDF2nEeoFmzUkj8LlX4KoUVUnzalgmqz0d4tisMtFyQwqh0i3zczI7azKeEq27OOf7okTARY4gered2__bf7kDt7o4mm23wL8La356D24erEhom_twRGKkUQJjySJVSOj3JxlG6uxzPK9gH9BmnnXFqOywlddp2GTKPmIIzcathgQhmX2aU_raAzi6lH49hPXpbOo3gAUXUidDcDmxsvHScOUxCuA2CCu5TweQ9OOrXUexTt081bjUIjzo83gYwMtV-3lLLnJhyzcEl1UrIgWPF2aLL7qzMTpg-I3RbKi9srjqDtZWKg0YcSuD35kpfB2BTZPpws9ypqvAwM4RCZjeRscoqfS6GMBmDzbd2bRG_0Xao3_ffgbXd8cH-3p_bzR8DDc4hoVtyuQmrC8X3_wTuOa-LyfN4mmcPgxOLhuXfwB_d1ma
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VLUJw4BuxUMAHEKdoE9v5OiBUKCtWpUsELSonYzs2WonuLpvl66_x65hJnEU9lFsPXBMriZOXmWd7_B7A44Q01nLrozQt6ggzVB0VSY5YFtrqzBpudWc2kU-nxfFxWW3B734vDJVV9jGxDdT1wtIc-YgXKVVjSslHPpRFVHvj58uvETlI0Uprb6fRQWTf_fqBw7fm2WQPv_UTzsevDl--joLDQGRlwtdRUuq0TH2iRWFSU8eJxgGFd7mUtdU6c9wYl2WFrGkx0WWpdyJucZ9hiLNSC7zuBdhGSi75ALaryUH1cTPDQ4qbRSI6pUghynikf84WJ03CYxJ5F6cyYWsYcFZaaHPd-Nr__Jauw9XAsNlu90vcgC03vwlXDjbytM0tOCKb0tYcY81aERHfz1wy5PDsQ7uSwd5iND0J21RZ1RnvNGw2Z--QXLPDzl2CMM7eL6mw7TYcnUu_7sBgvpi7u8C89bGV3tuU9Np4rnnpkB9w44WR3MVDiPpvrWwQX6duflE4CCNsqNPYGMLTTftlJztyZssXBJ1NK5ILbw8sVp9ViD7KIzFHnutrVxocj3tjijL2yMVLjc-ZlHg7Ap6ioIaPZXXYm4GdI3kwtYspU9Km7GwIOz3wVIh2jfqLunv_Pv0ILiEc1ZvJdP8-XObIF7tayh0YrFff3AO4aL-vZ83qYfiXGHw6b2D-AbWZZBs
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Constraint+Qualifications+for+Vector+Optimization+Problems+in+Real+Topological+Spaces&rft.jtitle=Axioms&rft.au=Zeng%2C+Renying&rft.date=2023-08-01&rft.issn=2075-1680&rft.eissn=2075-1680&rft.volume=12&rft.issue=8&rft.spage=783&rft_id=info:doi/10.3390%2Faxioms12080783&rft.externalDBID=n%2Fa&rft.externalDocID=10_3390_axioms12080783
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2075-1680&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2075-1680&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2075-1680&client=summon