DUALITY AND FARKAS-TYPE RESULTS FOR DC INFINITE PROGRAMMING WITH INEQUALITY CONSTRAINTS

In this paper, a DC infinite programming problem with inequality constraints is considered. By using the method of Fenchel conjugate functions, a dual scheme for the DC infinite programming problem is introduced. Then, under suitable conditions, weak and strong duality assertions are obtained. Moreo...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 4; pp. 1227 - 1244
Main Authors Sun, Xiang-Kai, Li, Sheng-Jie, Zhao, Dan
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2013
Subjects
Inequality constraints
Mathematical duality
Mathematical functions
Objective functions
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Summary:In this paper, a DC infinite programming problem with inequality constraints is considered. By using the method of Fenchel conjugate functions, a dual scheme for the DC infinite programming problem is introduced. Then, under suitable conditions, weak and strong duality assertions are obtained. Moreover, by using the obtained duality assertions, some Farkas-type results which characterize the optimal value of the DC infinite programming problem are given. As applications, the proposed approach is applied to conic programming problems. 2010Mathematics Subject Classification: 49N15, 90C32, 90C46. Key words and phrases: Duality, Conjugate function, Farkas-type results, DC infinite programming.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2675