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

Jinchuan Zhou; Changyu Wang; Naihua Xiu; Soonyi Wu

doi:10.3934/jimo.2009.5.851

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2009, Volume 5, Issue 4: 851-866. Doi: 10.3934/jimo.2009.5.851

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

1.
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044
2.
Institute of Operations Research, Qufu Normal University, Qufu 273165
3.
Department of Mathematics, National Cheng Kung University, Tainan 700

Received: December 31, 2007

Revised: May 31, 2009

Published: September 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C34, 90C46.

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

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