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K-epiderivatives for set-valued functions and optimization

Author

Listed:
  • Giancarlo Bigi
  • Marco Castellani

Abstract

Exploiting different tangent cones, many derivatives for set-valued functions have been introduced and considered to study optimality. The main goal of the paper is to address a general concept of K-epiderivative and to employ it to develop a quite general scheme for necesary optimality conditions in set-valued problems. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Giancarlo Bigi & Marco Castellani, 2002. "K-epiderivatives for set-valued functions and optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 401-412, June.
    • Handle: RePEc:spr:mathme:v:55:y:2002:i:3:p:401-412
    DOI: 10.1007/s001860200187
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    Citations

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    Cited by:

    1. Giovanni Crespi & Ivan Ginchev & Matteo Rocca, 2006. "First-order optimality conditions in set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 87-106, February.
    2. 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.
    3. 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.
    4. Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "First order optimality conditions in set-valued optimization," Economics and Quantitative Methods qf04010, Department of Economics, University of Insubria.
    5. S. J. Li & K. L. Teo & X. Q. Yang, 2008. "Higher-Order Optimality Conditions for Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 533-553, June.
    6. Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "First order optimality condition for constrained set-valued optimization," Economics and Quantitative Methods qf04014, Department of Economics, University of Insubria.
    7. P. Q. Khanh & N. D. Tuan, 2008. "Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 243-261, November.
    8. Zhenhua Peng & Zhongping Wan, 2020. "Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-23, March.

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