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On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities

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Abstract

In this paper, we consider a vector optimization problem involving approximately star-shaped functions. We formulate approximate vector variational inequalities in terms of Fréchet subdifferentials and solve the vector optimization problem. Under the assumptions of approximately straight functions, we establish necessary and sufficient conditions for a solution of approximate vector variational inequality to be an approximate efficient solution of the vector optimization problem. We also consider the corresponding weak versions of the approximate vector variational inequalities and establish various results for approximate weak efficient solutions.

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Acknowledgements

The research of the second author is supported by the Council of Scientific and Industrial Research, New Delhi, Ministry of Human Resources Development, Government of India Grant 20-06/2010 (i) EU-IV.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India

    S. K. Mishra & Vivek Laha

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  1. S. K. Mishra
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  2. Vivek Laha
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Correspondence to S. K. Mishra.

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Communicated by Guang-ya Chen.

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Mishra, S.K., Laha, V. On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities. J Optim Theory Appl 156, 278–293 (2013). https://doi.org/10.1007/s10957-012-0124-4

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