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Second-Order Optimality Conditions in Minimax Optimization Problems

Author

Listed:
  • Anulekha Dhara

    (Indian Institute of Technology Gandhinagar)

  • Aparna Mehra

    (Indian Institute of Technology Delhi)

Abstract

The paper primarily is concerned with the second-order optimality conditions for minimax problems, where the constraints are described by a set inclusion and a finite number of equalities, and where all the functions involved are Fréchet differentiable with locally Lipschitz derivatives. We make use of the Mangasarian Fromovitz regularity conditions and of the second-order Abadie regularity conditions.

Suggested Citation

  • Anulekha Dhara & Aparna Mehra, 2013. "Second-Order Optimality Conditions in Minimax Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 567-590, March.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0097-3
    DOI: 10.1007/s10957-012-0097-3
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    References listed on IDEAS

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    1. 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.
    2. Bienvenido Jiménez & Vicente Novo, 2003. "Second order necessary conditions in set constrained differentiable vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 299-317, November.
    3. T. Maeda, 2004. "Second-Order Conditions for Efficiency in Nonsmooth Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 521-538, September.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    Cited by:

    1. 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.
    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.

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