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Optimality Conditions and Duality in Nonsmooth Semiinfinite Programming |
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| Authors: | G. J. Zalmai Qinghong Zhang |
| Affiliation: | 1. Department of Mathematics and Computer Science , Northern Michigan University , Marquette , Michigan , USA gzalmai@nmu.edu;3. Department of Mathematics and Computer Science , Northern Michigan University , Marquette , Michigan , USA |
| Abstract: | In this article, we utilize the semiinfinite versions of Guignard's constraint qualification and Motzkin's theorem of the alternative to establish a set of Karush–Kuhn–Tucker-type necessary optimality conditions for a nonsmooth and nonconvex semiinfinite programming problem. Furthermore, we discuss some sufficient optimality conditions and duality relations for our semiinfinite programming problem. |
| Keywords: | Dual problems Duality theorems Generalized gradient Lipschitz function Necessary optimality conditions Nonsmooth function Semiinfinite programming Sufficient optimality conditions |