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On Multi-objective Optimization Problems and Vector Variational-Like Inequalities

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Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory (ICRAPAM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 307))

Abstract

This paper deals with nonsmooth multi-objective optimization problems involving locally Lipschitz \(V-r\)-invexity using Michel–Penot subdifferential. We consider vector variational-like inequalities of Stampacchia and Minty type and establish some results, which give necessary and sufficient conditions for a feasible point to be Pareto optimal solution of the MOP. We also establish various results related to weak Pareto optimal solution of the MOP and corresponding weak versions of the vector variational-like inequalities.

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Acknowledgements

The research of the first author 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).

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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

Authors
  1. Vivek Laha
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  2. Harsh Narayan Singh
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Corresponding author

Correspondence to Harsh Narayan Singh .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi, India

    Naokant Deo

  2. Department of Mathematics, Netaji Subhas University of Technology, New Delhi, India

    Vijay Gupta

  3. Department of Mathematics, Lucian Blaga University of Sibiu, Sibiu, Romania

    Ana Maria Acu

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

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Laha, V., Narayan Singh, H. (2020). On Multi-objective Optimization Problems and Vector Variational-Like Inequalities. In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 307. Springer, Singapore. https://doi.org/10.1007/978-981-15-1157-8_3

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