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Estimates of approximate solutions and well-posedness for variational inequalities

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  • Ya-Ping Fang
  • Rong Hu

Abstract

The purpose of this paper is to estimate the approximate solutions for variational inequalities. In terms of estimate functions, we establish some estimates of the sizes of the approximate solutions from outside and inside respectively. By considering the behaviors of estimate functions, we give some characterizations of the well-posedness for variational inequalities. Copyright Springer-Verlag 2007

Suggested Citation

  • Ya-Ping Fang & Rong Hu, 2007. "Estimates of approximate solutions and well-posedness for variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 281-291, April.
    • Handle: RePEc:spr:mathme:v:65:y:2007:i:2:p:281-291
    DOI: 10.1007/s00186-006-0122-0
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    References listed on IDEAS

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    1. M. B. Lignola, 2006. "Well-Posedness and L-Well-Posedness for Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 119-138, January.
    2. X. M. Yang & X. Q. Yang & K. L. Teo, 2004. "Some Remarks on the Minty Vector Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 193-201, April.
    3. X. X. Huang, 2001. "Extended and strongly extended well-posedness of set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 101-116, April.
    4. T. Zolezzi, 2001. "Well-Posedness and Optimization under Perturbations," Annals of Operations Research, Springer, vol. 101(1), pages 351-361, January.
    5. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
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    Cited by:

    1. Savin Treanţă, 2021. "On Well-Posedness of Some Constrained Variational Problems," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
    2. 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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