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Well-Posedness and Optimization under Perturbations

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  • T. Zolezzi

Abstract

Estimates of the size of sets of approximate solutions are obtained for well-posed optimization problems in a Banach space, and extended to problems subject to perturbations of a general form. An estimate of the perturbations guaranteeing a prescribed level of suboptimality is presented. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • T. Zolezzi, 2001. "Well-Posedness and Optimization under Perturbations," Annals of Operations Research, Springer, vol. 101(1), pages 351-361, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:351-361:10.1023/a:1010961617177
    DOI: 10.1023/A:1010961617177
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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. L. Q. Anh & P. Q. Khanh & D. T. M. Van, 2012. "Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 42-59, April.
    3. 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.
    4. Y. P. Fang & R. Hu & N. J. Huang, 2007. "Extended B-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 445-458, December.
    5. Li, Y.P. & Huang, G.H. & Guo, P. & Yang, Z.F. & Nie, S.L., 2010. "A dual-interval vertex analysis method and its application to environmental decision making under uncertainty," European Journal of Operational Research, Elsevier, vol. 200(2), pages 536-550, January.
    6. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    7. C. Lalitha & Prashanto Chatterjee, 2014. "Levitin–Polyak well-posedness for constrained quasiconvex vector optimization problems," Journal of Global Optimization, Springer, vol. 59(1), pages 191-205, May.

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