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Hölder continuity of perturbed solution set for convex optimization problems

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  • Li, X.B.
  • Li, S.J.

Abstract

In this paper, we first establish sufficient conditions for the local uniqueness and Hölder continuity of perturbed solution set for a scalar optimization problem. Then, by using a linear scalarization method, we obtain the Hölder continuity of two classes of perturbed solution sets for a multiobjective programming problem, respectively. We also give some examples to illustrate that our main results are applicable. These examples are also given to illustrate that our main results are new and different from the ones in literature.

Suggested Citation

  • Li, X.B. & Li, S.J., 2014. "Hölder continuity of perturbed solution set for convex optimization problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 908-918.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:908-918
    DOI: 10.1016/j.amc.2014.01.095
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    References listed on IDEAS

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    1. Li, S.J. & Chen, C.R. & Li, X.B. & Teo, K.L., 2011. "Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 148-157, April.
    2. L. Q. Anh & P. Q. Khanh, 2009. "Hölder Continuity of the Unique Solution to Quasiequilibrium Problems in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 37-54, April.
    3. 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.
    4. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    5. Li, S.J. & Li, X.B. & Wang, L.N. & Teo, K.L., 2009. "The Hölder continuity of solutions to generalized vector equilibrium problems," European Journal of Operational Research, Elsevier, vol. 199(2), pages 334-338, December.
    6. J. P. Evans & F. J. Gould, 1970. "Stability in Nonlinear Programming," Operations Research, INFORMS, vol. 18(1), pages 107-118, February.
    7. S. J. Li & X. B. Li, 2011. "Hölder Continuity of Solutions to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 540-553, June.
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