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Stability results for Ekeland's ε variational principle for vector valued functions

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  • G. Y. Chen
  • X. X. Huang

Abstract

In this paper, under the assumption that the nonconvex vector valued function f satisfies some lower semicontinuity property and bounded below, the nonconvex vector valued function sequence f n satisfies the same lower semicontinuity property and uniformly bounded below, and f n converges to f in the generalized sense of Mosco, we obtain the relation: , when , where when , C is the pointed closed convex dominating cone with nonempty interior int C, e∈int C. Under some conditions, we also prove the same result when f n converges to f in the generalized sense of Painleve'-Kuratowski. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • G. Y. Chen & X. X. Huang, 1998. "Stability results for Ekeland's ε variational principle for vector valued functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 97-103, September.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:1:p:97-103
    DOI: 10.1007/s001860050014
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    Cited by:

    1. Y N Wu & T C E Cheng, 2005. "Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 453-472, May.
    2. Xiao-Bing Li & Qi-Lin Wang & Zhi Lin, 2016. "Stability of Set-Valued Optimization Problems with Naturally Quasi-Functions," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 850-863, March.
    3. C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability for Properly Quasiconvex Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 492-506, November.

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