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Minimax fractional programming problem involving nonsmooth generalized α-univex functions

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DOI: 
10.11121/ijocta.01.2013.00102

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Abstract (Original Language): 
In this paper, we introduce a new class of generalized α-univex functions where the involved functions are locally Lipschitz. We extend the concept of α-type I invex [S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized α-type I invexity, J. Appl. Math. Comput. 31 (2009) 317-334] to α-univexity and an example is provided to show that there exist functions that are α-univex but not α-type I invex. Furthermore, Karush-Kuhn-Tuckertype sufficient optimality conditions and duality results for three different types of dual models are obtained for nondifferentiable minimax fractional programming problem involving generalized α- univex functions. The results in this paper extend some known results in the literature.
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