Optimization by Vector Space Methods
Optimization by Vector Space Methods
Error Bounds for Abstract Linear Inequality Systems
SIAM Journal on Optimization
A Nonlinear Extension of Hoffman's Error Bounds for Linear Inequalities
Mathematics of Operations Research
On First- and Second-Order Conditions\linebreak for Error Bounds
SIAM Journal on Optimization
Second-Order Sufficient Conditions for Error Bounds in Banach Spaces
SIAM Journal on Optimization
Error Bounds for Degenerate Cone Inclusion Problems
Mathematics of Operations Research
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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.