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Optimality and duality for second-order interval-valued variational problems

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Abstract

The paper studies the second-order interval-valued variational problem under \(\eta \)-bonvexity assumptions and proves the necessary optimality conditions. We investigate the functional which is \(\eta \)-bonvex but not invex. Further, we prove the duality theorems i.e. the weak and strong duality theorem to relate the values of the primal problem and dual problem. To validate the credibility of the weak duality theorem, we formulate an example of a second-order interval-valued variational problem.

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Acknowledgements

The authors would like to sincerely thank the referees for their valuable comments and suggestions, which significantly improved the paper’s readability. The authors acknowledge DST-FIST (Govt. of India) for the grant SR/FST/MS-1/2017/13 to support this research work. Also, the second author gratefully acknowledges technical support from the Seed Money Project TU/DORSP/57/7293 of TIET, Patiala.

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  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147 004, India

    Vivek Dhingra & N. Kailey

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  1. Vivek Dhingra
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  2. N. Kailey
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Dhingra, V., Kailey, N. Optimality and duality for second-order interval-valued variational problems. J. Appl. Math. Comput. 68, 3147–3162 (2022). https://doi.org/10.1007/s12190-021-01657-z

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  • DOI: https://doi.org/10.1007/s12190-021-01657-z

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