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- W2025833381 abstract "This paper studies local and global error bounds for a convex inequality defined by a proper convex function in a Banach space. The concept of weak basic constraint qualification (weak BCQ) is introduced to control the normal directions at a boundary point of the solution set. Local and global error bounds are characterized by a direction‐length decomposition condition, which provides a way to independently verify the weak BCQ and the length control of the subdifferential. To further characterize global error bounds, the segment extension property is proposed and studied. It is shown that the verification of the direction‐length condition for global error bounds can be sufficiently carried out on any subset having the segment extension property instead of the entire boundary. This leads to a simple formula for the smallest global error bound. In the Euclidean space, the verification of the condition and the computation of the smallest global error bound can be carried out on the set of extreme points." @default.
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- W2025833381 date "2007-01-01" @default.
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- W2025833381 title "Characterizations of Local and Global Error Bounds for Convex Inequalities in Banach Spaces" @default.
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- W2025833381 doi "https://doi.org/10.1137/050644872" @default.
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