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Lagrange multiplier rules for non-differentiable DC generalized semi-infinite programming problems

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  • Nader Kanzi

Abstract

This paper aims to study a broad class of generalized semi-infinite programming problems with (upper and lower level) objectives given as the difference of two convex functions, and (lower level) constraints described by a finite number of convex inequalities and a set constraints. First, we are interested in some various lower level constraint qualifications for the problem. Then, the results are used to establish efficient upper estimate of certain subdifferential of value functions. Finally, we apply the obtained subdifferential estimates to derive necessary optimality conditions for the problem. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Nader Kanzi, 2013. "Lagrange multiplier rules for non-differentiable DC generalized semi-infinite programming problems," Journal of Global Optimization, Springer, vol. 56(2), pages 417-430, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:417-430
    DOI: 10.1007/s10898-011-9828-5
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    References listed on IDEAS

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    1. Oliver Stein, 2001. "First-Order Optimality Conditions for Degenerate Index Sets in Generalized Semi-Infinite Optimization," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 565-582, August.
    2. J. J. Ye & S. Y. Wu, 2008. "First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 419-434, May.
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