On non-smooth α-invex functions and vector variational-like inequality |
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Authors: | S K Mishra S Y Wang K K Lai |
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Institution: | (1) Department of Mathematics, Statistics and Computer Science, College of Basic Sciences and Humanities, G. B. Pant University of Agriculture and Technology, Pantnagar, India;(2) Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China;(3) Department of Management Sciences, City University of Hong Kong, 83-Tat chee Avenue, Kowloon, Hong Kong SAR |
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Abstract: | In this paper, we establish some relationships between vector variational-like inequality and non-smooth vector optimization
problems under the assumptions of α-invex non-smooth functions. We identify the vector critical points, the weakly efficient points and the solutions of the
weak vector variational-like inequality, under non-smooth pseudo-α-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this
work extends an earlier work of Ruiz-Garzon et al. (J Oper Res 157:113–119, 2004) to a wider class of functions, namely the
non-smooth pseudo-α-invex functions. Moreover, this work extends an earlier work of Mishra and Noor (J Math Anal Appl 311:78–84, 2005) to non-differentiable
case. |
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Keywords: | Non-differentiable vector optimization Pseudo-α -invex functions Vector variational-like inequality |
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