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October  2009, 5(4): 851-866. doi: 10.3934/jimo.2009.5.851

First-order optimality conditions for convex semi-infinite min-max programming with noncompact sets

Jinchuan Zhou 1, , Changyu Wang 2, , Naihua Xiu 1, and  Soonyi Wu 3,

1. 

Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China, China
2. 

Institute of Operations Research, Qufu Normal University, Qufu 273165, China
3. 

Department of Mathematics, National Cheng Kung University, Tainan 700, Taiwan

Received  January 2008 Revised  June 2009 Published  August 2009

In this paper, based on some new characterizations of subderivative and subdifferential of sup-types functions, we develop the first-order necessary and sufficient optimality conditions for convex semi-infinite min-max programming problems in which the index sets are not necessarily compact.
Keywords: subderivative, first-order optimality conditions., subdifferential, semi-infinite programming.
Mathematics Subject Classification: Primary: 90C34, 90C4.
Citation: Jinchuan Zhou, Changyu Wang, Naihua Xiu, Soonyi Wu. First-order optimality conditions for convex semi-infinite min-max programming with noncompact sets. Journal of Industrial and Management Optimization, 2009, 5 (4) : 851-866. doi: 10.3934/jimo.2009.5.851
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