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On Global Error Bounds for Convex Inequalities Systems

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  • Vo Si Trong Long

    (University of Science
    Vietnam National University)

Abstract

In this paper, we first present necessary and sufficient conditions for the existence of global error bounds for a convex function without additional conditions on the function or the solution set. In particular, we obtain characterizations of such global error bounds in Euclidean spaces, which are often simple to check. Second, we prove that under a suitable assumption the subdifferential of the supremum function of an arbitrary family of convex continuous functions coincides with the convex hull of the subdifferentials of functions corresponding to the active indices at given points. As applications, we study the existence of global error bounds for infinite systems of linear and convex inequalities. Several examples are provided as well to explain the advantages of our results with existing ones in the literature.

Suggested Citation

  • Vo Si Trong Long, 2024. "On Global Error Bounds for Convex Inequalities Systems," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1359-1384, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02458-7
    DOI: 10.1007/s10957-024-02458-7
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    References listed on IDEAS

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    1. T. D. Chuong & V. Jeyakumar, 2017. "An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 203-226, April.
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    4. M. Volle & J. E. Martínez-Legaz & J. Vicente-Pérez, 2015. "Duality for Closed Convex Functions and Evenly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 985-997, December.
    5. Radu Boţ & Ernö Csetnek, 2012. "Error bound results for convex inequality systems via conjugate duality," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 296-309, July.
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