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Directionally generalized differentiation for multifunctions and applications to set-valued programming problems

Author

Listed:
  • Vo Duc Thinh

    (Dongthap University)

  • Thai Doan Chuong

    (Saigon University)

Abstract

The aim of this work is twofold. First, we establish sum rules for the directionally coderivatives of multifunctions and intersection rules for the directionally limiting normal cones. Then, we apply the provided formulas to derive directionally necessary conditions for a set-valued optimization problem with equilibrium constraints.

Suggested Citation

  • Vo Duc Thinh & Thai Doan Chuong, 2018. "Directionally generalized differentiation for multifunctions and applications to set-valued programming problems," Annals of Operations Research, Springer, vol. 269(1), pages 727-751, October.
    • Handle: RePEc:spr:annopr:v:269:y:2018:i:1:d:10.1007_s10479-017-2400-z
    DOI: 10.1007/s10479-017-2400-z
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    References listed on IDEAS

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    1. Thai Doan Chuong & Do Sang Kim, 2016. "A class of nonsmooth fractional multiobjective optimization problems," Annals of Operations Research, Springer, vol. 244(2), pages 367-383, September.
    2. T. Q. Bao & P. Gupta & B. S. Mordukhovich, 2007. "Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 179-203, November.
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    Cited by:

    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.

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