Primal Characterizations of Error Bounds for Composite-convex Inequalities
Abstract
This paper is devoted to primal conditions of error bounds for a general function. In terms of Bouligand tangent cones, lower Hadamard directional derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several necessary and/or sufficient conditions of error bounds with mild assumptions. Then we use these primal results to characterize error bounds for composite-convex functions (i.e. the composition of a convex function with a continuously differentiable mapping). It is proved that the primal characterization of error bounds can be established via Bouligand tangent cones, directional derivatives and the Hausdorff-Pompeiu excess if the mapping is metrically regular at the given point. The accurate estimate on the error bound modulus is also obtained.
Keywords
Cite
@article{arxiv.2210.00307,
title = {Primal Characterizations of Error Bounds for Composite-convex Inequalities},
author = {Zhou Wei and Michel Théra and Jen-Chih Yao},
journal= {arXiv preprint arXiv:2210.00307},
year = {2022}
}