Minimax fractional programming problem involving nonsmooth generalized α-univex functions

In this paper, we introduce a new class of generalized a-univex functions where the involved functions are locally Lipschitz. We extend the concept of a-type I invex [S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized a-type I invexity, J. Appl. Math....

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Published inAn international journal of optimization and control Vol. 3; no. 1; p. 7
Main Authors Jayswal, Anurag, Kumar, Rajnish, Kumar, Dilip
Format Journal Article
LanguageEnglish
Published Balikesir Balikesir University, Faculty of Engineering Department of Industrial Engineering 01.01.2013
Subjects
Mathematical programming
Minimax technique
Programming
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ISSN2146-0957
2146-5703
DOI10.11121/ijocta.01.2013.00102

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Summary:In this paper, we introduce a new class of generalized a-univex functions where the involved functions are locally Lipschitz. We extend the concept of a-type I invex [S. K. Mishra, J. S. Rautela, On nondifferentiable minimax fractional programming under generalized a-type I invexity, J. Appl. Math. Comput. 31 (2009) 317-334] to a-univexity and an example is provided to show that there exist functions that are a-univex but not a-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 a-univex functions. The results in this paper extend some known results in the literature.
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ISSN:2146-0957
2146-5703
DOI:10.11121/ijocta.01.2013.00102