SIAM Journal on Optimization, Volume 30, Issue 3, Page 2379-2409, January 2020.
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under parabolic regularity, a second-order regularity condition that was recently utilized in [A. Mohammadi, B. Mordukhovich, and M. E. Sarabi, Parabolic Regularity via Geometric Variational Analysis, preprint, ŭlhttps://arxiv.org/abs/1909.00241, 2019] for second-order variational analysis of constraint systems. Besides justifying the twice epi-differentiablity of composite functions, we obtain precise formulas for their second subderivatives under the metric subregularity constraint qualification. The latter allows us to derive second-order optimality conditions for a large class of composite optimization problems.

中文翻译：

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扩展实值函数的两次Epi可微性及其在复合优化中的应用

SIAM优化杂志，第30卷，第3期，第2379-2409页，2020年1月。
本文致力于扩展实值函数的两次表位可微性的研究，重点是满足某种复合表示的函数。这将在抛物线规则性下进行，抛物线规则性是最近在[A. Mohammadi，B。Mordukhovich和ME Sarabi，通过几何变分分析进行抛物线正则化，预印本，, lhttps：//arxiv.org/abs/1909.00241，2019]，用于约束系统的二阶变分分析。除了证明复合函数具有两倍的epi-可微性，我们还可以在度量次规则性约束条件下获得其二阶导数的精确公式。后者使我们能够针对大量的复合优化问题得出二阶最优条件。