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

Author

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  • Rishi Rajan Sahay

    (University of Delhi)

  • Guneet Bhatia

    (University of Delhi)

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.

Suggested Citation

  • Rishi Rajan Sahay & Guneet Bhatia, 2024. "Higher order strict global minimizers in non-differentiable multiobjective optimization involving higher order invexity and variational inequality," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 226-244, March.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:1:d:10.1007_s12597-023-00670-z
    DOI: 10.1007/s12597-023-00670-z
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    References listed on IDEAS

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    1. S. K. Mishra & Vivek Laha, 2013. "On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 278-293, February.
    2. G.H. Lin & M. Fukushima, 2003. "Some Exact Penalty Results for Nonlinear Programs and Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 67-80, July.
    3. S. K. Mishra & Vivek Laha, 2013. "A Note on the Paper “On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities”," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 554-557, November.
    4. M. Golestani & H. Sadeghi & Y. Tavan, 2018. "Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 896-916, December.
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