On approximate vector variational inequalities and vector optimization problem using convexificator

Faizan A. Khan; Rohit K. Bhardwaj; Tirth Ram; Mohammed A. S. Tom; Faizan A. Khan; Rohit K. Bhardwaj; Tirth Ram; Mohammed A. S. Tom

doi:10.3934/math.20221039

AIMS Mathematics

2022, Volume 7, Issue 10: 18870-18882. doi: 10.3934/math.20221039

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Research article

On approximate vector variational inequalities and vector optimization problem using convexificator

1.
Computational & Analytical Mathematics and their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Kingdom of Saudi Arabia
2.
Department of Mathematics, University of Jammu, Jammu 180006, India
3.
Department of Mathematics, University of Bahri, Khartoum 11111, Sudan

Received: 31 May 2022 Revised: 05 August 2022 Accepted: 07 August 2022 Published: 25 August 2022
MSC : 58E17, 49J40, 49J52

In the present article, we study a vector optimization problem involving convexificator-based locally Lipschitz approximately convex functions and give some ideas for approximate efficient solutions. In terms of the convexificator, we approximate Stampacchia-Minty type vector variational inequalities and use them to describe an approximately efficient solution to the nonsmooth vector optimization problem. Moreover, we give a numerical example that attests to the credibility of our results.
- approximate efficient solutions,
- convexificator,
- nonsmooth vector optimization problem,
- vector variational inequality
Citation: Faizan A. Khan, Rohit K. Bhardwaj, Tirth Ram, Mohammed A. S. Tom. On approximate vector variational inequalities and vector optimization problem using convexificator[J]. AIMS Mathematics, 2022, 7(10): 18870-18882. doi: 10.3934/math.20221039

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Abstract

In the present article, we study a vector optimization problem involving convexificator-based locally Lipschitz approximately convex functions and give some ideas for approximate efficient solutions. In terms of the convexificator, we approximate Stampacchia-Minty type vector variational inequalities and use them to describe an approximately efficient solution to the nonsmooth vector optimization problem. Moreover, we give a numerical example that attests to the credibility of our results.

References

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