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Well-Posedness by Perturbations of Variational Problems

Author

Listed:
  • B. Lemaire

    (Université de Montpellier II)

  • C. Ould Ahmed Salem

    (Université des Sciences et Techniques)

  • J. P. Revalski

    (Institute of Mathematics and Informatics)

Abstract

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.

Suggested Citation

  • B. Lemaire & C. Ould Ahmed Salem & J. P. Revalski, 2002. "Well-Posedness by Perturbations of Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 345-368, November.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:2:d:10.1023_a:1020840322436
    DOI: 10.1023/A:1020840322436
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    Citations

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    Cited by:

    1. Ya-ping Fang & Nan-jing Huang, 2007. "Increasing-along-rays property, vector optimization and well-posedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 99-114, February.
    2. San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    3. Yi-bin Xiao & Nan-jing Huang, 2011. "Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 33-51, October.
    4. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.

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