Regularity conditions characterizing Fenchel-Lagrange duality and Farkas-type results in DC infinite programming

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• 作者：Xiang-Kai Sun ^{xksun@126.com" class="auth_mail sxkcqu@163.com" class="auth_mail}
• 关键词：DC infinite programming ; Regularity conditions ; Fenchel&ndash ; Lagrange duality ; Farkas-type results ; Conic programming
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：15 June, 2014
• 年：2014
• 卷：414
• 期：2
• 页码：590-611
• 全文大小：351 K

文摘

In this paper, we consider a DC infinite programming problem (P) with inequality constraints. By using the properties of the epigraph of the conjugate functions, we introduce some new notions of regularity conditions for (P). Under these new regularity conditions, we completely characterize the Fenchel-Lagrange duality and the stable Fenchel-Lagrange duality for (P). Similarly, we also completely characterize the Farkas-type results and the stable Farkas-type results for (P). As applications, we obtain the corresponding results for conic programming problems.