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Generalized higher-order cone-convex functions and higher-order duality in vector optimization

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  • S. K. Suneja

    (University of Delhi)

  • Sunila Sharma

    (University of Delhi)

  • Priyanka Yadav

    (University of Delhi)

Abstract

In this paper, we introduce a new class of higher-order cone-convex, $$(K_1, K_2)$$ ( K 1 , K 2 ) -pseudoconvex and quasiconvex functions which encapsulates several already known functions. Higher-order sufficient optimality conditions have been established for a vector optimization problem over cones by using these functions, under weaker conditions on multipliers as compared to other papers in this domain. Wolfe type and Mond–Weir type higher-order duals are formulated and corresponding duality results are established. A number of previously studied problems appear as special cases of our primal-dual models. In case of nonlinear programming problem, our higher-order duals reduce to the corresponding higher-order duals given by Mangasarian (J Math Anal Appl 51:607–620, 1975) and Mond and Zhang (Generalized convexity, generalized monotonicity: recent results. Kluwer, Dordrecht, pp 357–372, 1998).

Suggested Citation

  • S. K. Suneja & Sunila Sharma & Priyanka Yadav, 2018. "Generalized higher-order cone-convex functions and higher-order duality in vector optimization," Annals of Operations Research, Springer, vol. 269(1), pages 709-725, October.
    • Handle: RePEc:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2470-y
    DOI: 10.1007/s10479-017-2470-y
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    References listed on IDEAS

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    1. S. Askar & A. Tiwari, 2009. "First-order optimality conditions and duality results for multi-objective optimisation problems," Annals of Operations Research, Springer, vol. 172(1), pages 277-289, November.
    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.
    4. Altannar Chinchuluun & Dehui Yuan & Panos Pardalos, 2007. "Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity," Annals of Operations Research, Springer, vol. 154(1), pages 133-147, October.
    5. Gutiérrez, C. & Jiménez, B. & Novo, V. & Ruiz-Garzón, G., 2015. "Efficiency through variational-like inequalities with Lipschitz functions," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 438-449.
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    Cited by:

    1. Thai Doan Chuong, 2021. "Optimality and duality in nonsmooth composite vector optimization and applications," Annals of Operations Research, Springer, vol. 296(1), pages 755-777, January.

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