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Stability for Properly Quasiconvex Vector Optimization Problem

Author

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  • C. S. Lalitha

    (University of Delhi South Campus)

  • Prashanto Chatterjee

    (University of Delhi)

Abstract

The aim of this paper is to study the stability aspects of various types of solution set of a vector optimization problem both in the given space and in its image space by perturbing the objective function and the feasible set. The Kuratowski–Painlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems to the corresponding minimal set of the original problem is established assuming the objective functions to be (strictly) properly quasi cone-convex.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0079-5
    DOI: 10.1007/s10957-012-0079-5
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    References listed on IDEAS

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    1. G. P. Crespi & A. Guerraggio & M. Rocca, 2007. "Well Posedness in Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 213-226, January.
    2. 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.
    3. E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
    4. Hedy Attouch & Hassan Riahi, 1993. "Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 173-201, February.
    5. X. X. Huang, 2000. "Stability in vector-valued and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 185-193, November.
    6. G. P. Crespi & M. Papalia & M. Rocca, 2009. "Extended Well-Posedness of Quasiconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 285-297, May.
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    Citations

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    Cited by:

    1. 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.
    2. Shiva Kapoor & C. S. Lalitha, 2019. "Stability in unified semi-infinite vector optimization," Journal of Global Optimization, Springer, vol. 74(2), pages 383-399, June.
    3. Shiva Kapoor & C. S. Lalitha, 2019. "Stability and Scalarization for a Unified Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1050-1067, September.
    4. C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability and Scalarization of Weak Efficient, Efficient and Henig Proper Efficient Sets Using Generalized Quasiconvexities," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 941-961, December.
    5. C. S. Lalitha & Prashanto Chatterjee, 2015. "Stability and Scalarization in Vector Optimization Using Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 825-843, September.

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