论文标题
两次不可分割的功能的两次分辨率和抛物线的规律性
Twice epi-differentiablity and parabolic regularity of a class of non-amenable functions
论文作者
论文摘要
本文涉及一类不符合功能的两倍分化性和抛物面的规律性，分段的组成两倍（PWTD）函数（PWTD）功能以及抛物面的半分化映射。这种综合功能通常出现在复合优化问题，分离优化问题以及较低和/或稀疏优化问题中。通过建立PWTD函数的两倍的表E-差异性和抛物线差异性，我们证明了该类别的复合函数的抛物线抛物性Epi-差异性，以及在抛物线寄生虫规律性假设下的Epi差异性差异。然后，我们确定一种条件，借助于其第二个亚衍生物的上层和下部估计，以确保其抛物线规则性，并证明该条件适用于几类特定的不符合性功能。
This paper concerns the twice epi-differentiability and parabolic regularity of a class of non-amenable functions, the composition of a piecewise twice differentiable (PWTD) function and a parabolically semidifferentiable mapping. Such composite functions often appear in composite optimization problems, disjunctive optimization problems, and low-rank and/or sparsity optimization problems. By establishing the proper twice epi-differentiability and parabolic epi-differentiability of PWTD functions, we prove the parabolic epi-differentiability of this class of composite functions, and its twice epi-differentiability under the parabolic regularity assumption. Then, we identify a condition to ensure its parabolic regularity with the help of an upper and lower estimate of its second subderivative, and demonstrate that this condition holds for several classes of specific non-amenable functions.
