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On minty variational principle for nonsmooth vector optimization problems with approximate convexity

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Abstract

In this paper, we consider a vector optimization problem involving locally Lipschitz approximately convex functions and give several concepts of approximate efficient solutions. We formulate approximate vector variational inequalities of Stampacchia and Minty type and use these inequalities as a tool to characterize an approximate efficient solution of the vector optimization problem.

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Acknowledgments

The authors are thankful to Prof. Dinh The Luc for his remarkable suggestions and fruitful discussions on an earlier version of this paper which helped to improve the quality of this paper in its present form. The authors are also thankful to the anonymous referees of this paper whose valuable comments helped to discuss future direction of the research work based on this paper. The research of Vivek Laha was supported by the Council of Scientific and Industrial Research, New Delhi, Ministry of Human Resources Development, Government of India through CSIR-UGC Fellowship (Ref. No. 20-06/2010 (i) EU-IV) during the preparation of this manuscript. At present Vivek Laha is supported by NBHM Postdoctoral Fellowship of Department of Atomic Energy, Government of India (Ref. No. 2/40(47)/2014/R&D-II/1170).

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  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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Mishra, S.K., Laha, V. On minty variational principle for nonsmooth vector optimization problems with approximate convexity. Optim Lett 10, 577–589 (2016). https://doi.org/10.1007/s11590-015-0883-6

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