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Generalized second-order contingent epiderivatives in parametric vector optimization problems

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  • Xiang-Kai Sun
  • Sheng-Jie Li

Abstract

This paper is concerned with generalized second-order contingent epiderivatives of frontier and solution maps in parametric vector optimization problems. Under some mild conditions, we obtain some formulas for computing generalized second-order contingent epiderivatives of frontier and solution maps, respectively. We also give some examples to illustrate the corresponding results. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Xiang-Kai Sun & Sheng-Jie Li, 2014. "Generalized second-order contingent epiderivatives in parametric vector optimization problems," Journal of Global Optimization, Springer, vol. 58(2), pages 351-363, February.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:2:p:351-363
    DOI: 10.1007/s10898-013-0054-1
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    References listed on IDEAS

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    1. Guang Ya Chen & Johannes Jahn, 1998. "Optimality conditions for set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 187-200, November.
    2. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
    3. S. J. Li & S. K. Zhu & K. L. Teo, 2012. "New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 587-604, March.
    4. J. Jahn & A. A. Khan & P. Zeilinger, 2005. "Second-Order Optimality Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 331-347, May.
    5. T. D. Chuong & J. C. Yao, 2010. "Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 77-94, July.
    6. M. H. Li & S. J. Li, 2010. "Second-Order Differential and Sensitivity Properties of Weak Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 76-87, January.
    7. S. J. Li & Hong Yan & G. Y. Chen, 2003. "Differential and sensitivity properties of gap functions for vector variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 377-391, August.
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