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Higher order strict global minimizers in non-differentiable multiobjective optimization involving higher order invexity and variational inequality

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Abstract

In this paper, we introduce new classes of higher order generalized strong invex functions under non-differentiable settings. The optimality results are derived for higher order strict global minimizers of non-differentiable multiobjective programming problems using these functions. Numerical examples and illustrations are provided in support of new classes of functions and the optimality conditions. We also study the mixed dual problem and establish weak, strong and converse duality results. Furthermore, as an application, we present a non-differentiable case of vector variational-like inequality problem and establish the equivalence between its solutions and higher order strict global minimizers of the non-differentiable multiobjective programming problem.

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Acknowledgements

The authors would like to thank Prof. Davinder Bhatia (Retd.) and Prof. Pankaj Gupta, Department of Operational Research, University of Delhi for their keen interest and continuous help throughout the preparation of this article. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors would like to thank the editor and anonymous reviewers for their comments that helped improve the quality of this work.

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  1. Shaheed Sukhdev College of Business Studies, University of Delhi, New Delhi, India

    Rishi Rajan Sahay

  2. Lakshmibai College, University of Delhi, New Delhi, India

    Guneet Bhatia

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  1. Rishi Rajan Sahay
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Sahay, R.R., Bhatia, G. Higher order strict global minimizers in non-differentiable multiobjective optimization involving higher order invexity and variational inequality. OPSEARCH 61, 226–244 (2024). https://doi.org/10.1007/s12597-023-00670-z

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