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KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions

Author

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  • Singh, D.
  • Dar, B.A.
  • Kim, D.S.

Abstract

We devote this paper to study a class of interval valued multiobjective programming problems. For this we consider two order relations LU and LS on the set of all closed intervals and propose many concepts of Pareto optimal solutions. Based on convexity concepts (viz. LU and LS-convexity) and generalized differentiability (viz. gH-differentiability) of interval valued functions, the KKT optimality conditions for aforesaid problems are obtained. In addition, we compare our results with the results given in Wu (2009) and we show some advantages of our results. The theoretical development is illustrated by suitable examples.

Suggested Citation

  • Singh, D. & Dar, B.A. & Kim, D.S., 2016. "KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions," European Journal of Operational Research, Elsevier, vol. 254(1), pages 29-39.
    • Handle: RePEc:eee:ejores:v:254:y:2016:i:1:p:29-39
    DOI: 10.1016/j.ejor.2016.03.042
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    Cited by:

    1. Fabiola Roxana Villanueva & Valeriano Antunes Oliveira, 2022. "Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 896-923, September.
    2. Khan, Muhammad Bilal & Santos-García, Gustavo & Noor, Muhammad Aslam & Soliman, Mohamed S., 2022. "Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţǎ, Savin, 2023. "Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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