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Optimality and duality for vector optimization problem with non-convex feasible set

Author

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  • S. K. Suneja

    (University of Delhi)

  • Sunila Sharma

    (University of Delhi)

  • Priyanka Yadav

    (University of Delhi)

Abstract

The Karush–Kuhn–Tucker (KKT) optimality conditions are necessary and sufficient for a convex programming problem under suitable constraint qualification. Recently, several papers (Dutta and Lalitha in Optim Lett 7(2):221–229, 2013; Lasserre in Optim Lett 4(1):1–5, 2010; Suneja et al. Am J Oper Res 3(6):536–541, 2013) have appeared wherein the convexity of constraint function has been replaced by convexity of the feasible set. Further, Ho (Optim Lett 11(1):41–46, 2017) studied nonlinear programming problem with non-convex feasible set. We have used this modified approach in the present paper to study vector optimization problem over cones. The KKT optimality conditions are proved by replacing the convexity of the objective function with convexity of strict level set, convexity of feasible set is replaced by a weaker condition and no condition is assumed on the constraint function. We have also formulated a Mond–Weir type dual and proved duality results in the modified setting. Our results directly extend the work of Ho (2017) Suneja et al. (2013) and Lasserre (2010).

Suggested Citation

  • S. K. Suneja & Sunila Sharma & Priyanka Yadav, 2020. "Optimality and duality for vector optimization problem with non-convex feasible set," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 1-12, March.
    • Handle: RePEc:spr:opsear:v:57:y:2020:i:1:d:10.1007_s12597-019-00401-3
    DOI: 10.1007/s12597-019-00401-3
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    References listed on IDEAS

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    1. Khanh, Phan Quoc & Quyen, Ho Thuc & Yao, Jen-Chih, 2011. "Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials," European Journal of Operational Research, Elsevier, vol. 212(2), pages 235-241, July.
    2. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    3. Suneja, S. K. & Aggarwal, Sunila & Davar, Sonia, 2002. "Multiobjective symmetric duality involving cones," European Journal of Operational Research, Elsevier, vol. 141(3), pages 471-479, September.
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