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Second order sufficient optimality conditions in vector optimization

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  • Ning E.
  • Wen Song
  • Yu Zhang

Abstract

In this paper, we mainly consider second-order sufficient conditions for vector optimization problems. We first present a second-order sufficient condition for isolated local minima of order 2 to vector optimization problems and then prove that the second-order sufficient condition can be simplified in the case where the constrained cone is a convex generalized polyhedral and/or Robinson’s constraint qualification holds. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Ning E. & Wen Song & Yu Zhang, 2012. "Second order sufficient optimality conditions in vector optimization," Journal of Global Optimization, Springer, vol. 54(3), pages 537-549, November.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:537-549
    DOI: 10.1007/s10898-011-9776-0
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    References listed on IDEAS

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    1. B. Aghezzaf & M. Hachimi, 1999. "Second-Order Optimality Conditions in Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 37-50, July.
    2. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    3. Giancarlo Bigi, 2006. "On sufficient second order optimality conditions in multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 77-85, February.
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    Cited by:

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    2. Yi-Hong Xu & Zhen-Hua Peng, 2018. "Second-Order M-Composed Tangent Derivative and Its Applications," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-20, October.
    3. Zhenhua Peng & Yihong Xu, 2017. "New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 128-140, January.
    4. Nguyen Thi Toan & Le Quang Thuy & Nguyen Tuyen & Yi-Bin Xiao, 2021. "Second-order KKT optimality conditions for multiobjective discrete optimal control problems," Journal of Global Optimization, Springer, vol. 79(1), pages 203-231, January.
    5. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    6. Bui Trong Kien & Trinh Duy Binh, 2023. "On the second-order optimality conditions for multi-objective optimal control problems with mixed pointwise constraints," Journal of Global Optimization, Springer, vol. 85(1), pages 155-183, January.

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