Global error bound for convex inclusion problems |
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Authors: | Yiran He |
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Institution: | (1) Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, 610068, China |
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Abstract: | The existence of global error bound for convex inclusion problems is discussed in this paper, including pointwise global error
bound and uniform global error bound. The existence of uniform global error bound has been carefully studied in Burke and
Tseng (SIAM J. Optim. 6(2), 265–282, 1996) which unifies and extends many existing results. Our results on the uniform global
error bound (see Theorem 3.2) generalize Theorem 9 in Burke and Tseng (1996) by weakening the constraint qualification and
by widening the varying range of the parameter. As an application, the existence of global error bound for convex multifunctions
is also discussed. |
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Keywords: | Error bound Convex inclusion Convex multifunction |
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