Optimality conditions and duality for semi-infinite programming involving semilocally type I-preinvex and related functions
Commun. Korean Math. Soc. 2012 Vol. 27, No. 2, 411-423
https://doi.org/10.4134/CKMS.2012.27.2.411
Printed June 1, 2012
Monika Jaiswal, Shashi Kant Mishra, and Bader Al Shamary
Banaras Hindu University, Banaras Hindu University, Kuwait University
Abstract : A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are $\eta$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-infinite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.
Keywords : multiobjective programming, semi-infinite programming, optimality, duality
MSC numbers : 90C29, 90C34, 90C46
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