Global error bound for convex inclusion problems
Journal of Global Optimization
Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces
SIAM Journal on Optimization
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In a recent paper Li and Singer (1998) introduced the notion of global error bound for a convex multifunction at a point of its domain. They showed the existence of such a global error bound when the image of the multifunction at the respective point is bounded and conjectured a result for the case when the image is not bounded. In this paper we solve their conjecture with a positive answer. For this we establish a criterion for the existence of a global error bound using the Pompeiu-Hausdorff excess. We also improve slightly some results of Li and Singer and introduce a gage associated to a multifunction similar to that for well-conditioning of convex functions, with similar properties.