论文标题
复合征符不平等的误差边界的原始特征
Primal Characterizations of Error Bounds for Composite-convex Inequalities
论文作者
论文摘要
本文致力于普通函数的原始误差界条件。就布里甘派切线，下哈马德定向衍生物和豪斯多夫庞贝的子集的过量而言，我们提供了一些带有轻度假设的误差界条件。然后，我们使用这些原始结果来表征复合符号函数的误差界（即，具有连续可区分的映射的凸函数的组成）。事实证明，如果在给定点上映射定期定期，则可以通过布利加人切线，定向衍生物和hausdorff-pompeiu多余的原始表征来确定误差边界的原始表征。还获得了对误差结合模量的准确估计。
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.
