On Constraint Qualification for an Infinite System of Quasiconvex Inequalities in Normed Linear Space

The constraint qualification Q-CCCQ plays an important role in quasiconvex programming and has been developed by many authors to investigate the set containment problem, duality and optimality conditions for quasiconvex programming. In this paper, we consider an infinite quasiconvex inequality syste...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 20; no. 3; pp. 685 - 697
Main Author Zhao, Xiaopeng
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2016
Subjects
Index sets
Mathematical duality
Mathematical functions
Mathematical inequalities
Necessary conditions
Sufficient conditions
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Summary:The constraint qualification Q-CCCQ plays an important role in quasiconvex programming and has been developed by many authors to investigate the set containment problem, duality and optimality conditions for quasiconvex programming. In this paper, we consider an infinite quasiconvex inequality system defined by a family of proper lower semicontinuous quasiconvex functions {hi :i∈I} and establish some sufficient conditions for ensuring the Q-CCCQ in terms of the interior-point condition together with approximate continuity assumption of the functioni↦hi (x). 2010Mathematics Subject Classification. 90C25, 90C26, 90C46. Key words and phrases. Quasiconvex programming, Constraint qualification, Interior-point condition.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.6713