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Optimality Conditions in Quasidifferentiable Vector Optimization

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  • T. Antczak

    (University of Łódź)

Abstract

In the paper, the quasidifferentiable vector optimization problem with the inequality constraints is considered. The Fritz John-type necessary optimality conditions and the Karush–Kuhn–Tucker-type necessary optimality conditions for a weak Pareto solution are derived for such a nonsmooth vector optimization problem. Further, the concept of an F-convex function with respect to a convex compact set is introduced. Then, the sufficient optimality conditions for a (weak) Pareto optimality of a feasible solution are established for the considered nonsmooth multiobjective optimization problem under assumptions that the involved functions are quasidifferentiable F-convex with respect to convex compact sets which are equal to Minkowski sum of their subdifferentials and superdifferentials at this point.

Suggested Citation

  • T. Antczak, 2016. "Optimality Conditions in Quasidifferentiable Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 708-725, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0987-x
    DOI: 10.1007/s10957-016-0987-x
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    References listed on IDEAS

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    1. A. J. V. Brandão & M. A. Rojas-Medar & G. N. Silva, 1999. "Optimally Conditions for Pareto Nonsmooth Nonconvex Programming in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 65-73, October.
    2. Y. Gao, 2000. "Demyanov Difference of Two Sets and Optimality Conditions of Lagrange Multiplier Type for Constrained Quasidifferentiable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 377-394, February.
    3. N. J. Huang & J. Li & S. Y. Wu, 2009. "Optimality Conditions for Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 323-342, August.
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    Cited by:

    1. Vivek Laha & Harsh Narayan Singh, 2023. "On quasidifferentiable mathematical programs with equilibrium constraints," Computational Management Science, Springer, vol. 20(1), pages 1-20, December.
    2. Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.
    3. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.

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