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On nonsmooth V-invexity and vector variational-like inequalities in terms of the Michel–Penot subdifferentials

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Abstract

In this paper, we establish some results which exhibit an application for Michel–Penot subdifferential in nonsmooth vector optimization problems and vector variational-like inequalities. We formulate vector variational-like inequalities of Stampacchia and Minty type in terms of the Michel–Penot subdifferentials and use these variational-like inequalities as a tool to solve the vector optimization problem involving nonsmooth V-invex function. We also consider the corresponding weak versions of the vector variational-like inequalities and establish various results for the weak efficient solutions.

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Acknowledgments

The research of Vivek Laha 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

    Vivek Laha & S. K. Mishra

  2. Department of Mathematics and Computer Science, Kuwait University, Kuwait, Kuwait

    Bader Al-Shamary

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  1. Vivek Laha
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  2. Bader Al-Shamary
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  3. S. K. Mishra
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Correspondence to S. K. Mishra.

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Laha, V., Al-Shamary, B. & Mishra, S.K. On nonsmooth V-invexity and vector variational-like inequalities in terms of the Michel–Penot subdifferentials. Optim Lett 8, 1675–1690 (2014). https://doi.org/10.1007/s11590-013-0707-5

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