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Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Author

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  • Xiangkai Sun

    (Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

  • Hongyong Fu

    (China Research Institute of Enterprise Governed by Law, Southwest University of Political Science and Law, 301 Baosheng Street, Chongqing 401120, China)

  • Jing Zeng

    (Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

Abstract

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

Suggested Citation

  • Xiangkai Sun & Hongyong Fu & Jing Zeng, 2018. "Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:12-:d:192760
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    References listed on IDEAS

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    1. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
    2. V. Jeyakumar & G. M. Lee & G. Li, 2015. "Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 407-435, February.
    3. Radu Ioan Bot, 2010. "Conjugate Duality in Convex Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-04900-2, July.
    4. Fakhar, Majid & Mahyarinia, Mohammad Reza & Zafarani, Jafar, 2018. "On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 265(1), pages 39-48.
    5. V. Jeyakumar, 1997. "Asymptotic Dual Conditions Characterizing Optimality for Infinite Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 153-165, April.
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    Cited by:

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