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On Minimax Programming with Vanishing Constraints

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Optimization, Variational Analysis and Applications (IFSOVAA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 355))

Abstract

In this chapter, we deal with a class of minimax programming problems with vanishing constraints. We establish necessary and sufficient optimality results for such a feasible point to be an optimal solution. Moreover, we formulate Mond–Weir type dual model for such a minimax programming problem with vanishing constraints and obtain various duality results. Also, we apply some results obtained for minimax programming problem with vanishing constraints to a multiobjective optimization problem with vanishing constraints.

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Acknowledgements

The authors are thankful to the anonymous referees who helped to improve the presentation of this chapter in its present form. The research of Dr. Vivek Laha is supported by UGC-BSR start up grant by University Grant Commission, New Delhi, India (Letter No. F.30-370/2017(BSR)) (Project No. M-14-40). The research of Prof. S.K. Mishra is supported by Department of Science and Technology, SERB, New Delhi, India through grant no.: MTR/2018/000121.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Vivek Laha, Harsh Narayan Singh & S. K. Mishra

  2. Department of Mathematics, Government Chandravijay College, Dindori, 481880, India

    Rahul Kumar

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  1. Vivek Laha
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  2. Rahul Kumar
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  3. Harsh Narayan Singh
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  4. S. K. Mishra
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Correspondence to Vivek Laha .

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Editors and Affiliations

  1. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    Vivek Laha

  2. Institut de Mathématiques de Toulouse, Paul Sabatier University, Toulouse, France

    Pierre Maréchal

  3. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    S. K. Mishra

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Laha, V., Kumar, R., Singh, H.N., Mishra, S.K. (2021). On Minimax Programming with Vanishing Constraints. In: Laha, V., Maréchal, P., Mishra, S.K. (eds) Optimization, Variational Analysis and Applications. IFSOVAA 2020. Springer Proceedings in Mathematics & Statistics, vol 355. Springer, Singapore. https://doi.org/10.1007/978-981-16-1819-2_11

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