# OPTIMALITY CONDITIONS AND DUALITY FOR SEMI-INFINITE PROGRAMMING INVOLVING SEMILOCALLY TYPE I-PREINVEX AND RELATED FUNCTIONS

• Jaiswal, Monika (DST-Centre for Interdisciplinary Mathematical Sciences Department of Mathematics Banaras Hindu University) ;
• Mishra, Shashi Kant (DST-Centre for Interdisciplinary Mathematical Sciences Department of Mathematics Banaras Hindu University) ;
• Al Shamary, Bader (Department of Mathematics Kuwait University)
• Published : 2012.04.30

#### 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-in nite 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.

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#### Cited by

1. Duality models for multiobjective semiinfinite fractional programming problems involving type-I and related functions pp.1727-933X, 2018, https://doi.org/10.2989/16073606.2018.1509906