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Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability

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  • N. Q. Huy

    (Hanoi Pedagogical University No. 2)

  • J.-C. Yao

    (National Sun Yat-sen University)

Abstract

This paper is devoted to the study of the stability of the solution map for the parametric convex semi-infinite optimization problem under convex function perturbations in short, PCSI. We establish sufficient conditions for the pseudo-Lipschitz property of the solution map of PCSI under perturbations of both objective function and constraint set. The main result obtained is new even when the problems under consideration reduce to linear semi-infinite optimization. Examples are given to illustrate the obtained results.

Suggested Citation

  • N. Q. Huy & J.-C. Yao, 2011. "Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 237-256, February.
    • Handle: RePEc:spr:joptap:v:148:y:2011:i:2:d:10.1007_s10957-010-9753-7
    DOI: 10.1007/s10957-010-9753-7
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    References listed on IDEAS

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    1. María J. Cánovas & Marco A. López & Juan Parra & F. Javier Toledo, 2006. "Lipschitz Continuity of the Optimal Value via Bounds on the Optimal Set in Linear Semi-Infinite Optimization," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 478-489, August.
    2. Goberna, M.A. & Gomez, S. & Guerra, F. & Todorov, M.I., 2007. "Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1069-1085, September.
    3. T. Son & N. Dinh, 2008. "Characterizations of optimal solution sets of convex infinite programs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 147-163, July.
    4. M. J. Cánovas & A. Hantoute & M. A. López & J. Parra, 2008. "Stability of Indices in the KKT Conditions and Metric Regularity in Convex Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 485-500, December.
    5. T. Chuong & N. Huy & J. Yao, 2009. "Stability of semi-infinite vector optimization problems under functional perturbations," Computational Optimization and Applications, Springer, vol. 45(4), pages 583-595, December.
    6. Chuong, T.D. & Huy, N.Q. & Yao, J.C., 2010. "Pseudo-Lipschitz property of linear semi-infinite vector optimization problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 639-644, February.
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    Cited by:

    1. 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.
    2. Zai-Yun Peng & Jian-Wen Peng & Xian-Jun Long & Jen-Chih Yao, 2018. "On the stability of solutions for semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 70(1), pages 55-69, January.
    3. N. Huy & D. Kim, 2013. "Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 56(2), pages 431-448, June.

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