First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems

J. J. Ye () and S. Y. Wu
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J. J. Ye: University of Victoria
S. Y. Wu: National Cheng-Kung University

Journal of Optimization Theory and Applications, 2008, vol. 137, issue 2, No 11, 419-434

Abstract: Abstract We study first-order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various well-known constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs takes a weaker form unless a certain constraint qualification is satisfied. In the completely convex case where the objective of the lower-level problem is concave and the constraint functions are quasiconvex, we show that the KKT condition takes a sharper form.

Keywords: Necessary optimality conditions; Constraint qualifications; Nonsmooth analysis; Value function; Generalized semi-infinite programming problems (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-008-9352-z

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