An extension of Attouch’s theorem and its application to second-order epi-differentiation of convexly composite functions
An extension of Attouch’s theorem and its application to second-order epi-differentiation of convexly composite functions
复制标题
Attouch定理的推广及其在凸复合函数二阶外延微分中的应用
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
R. Poliquin
中科院分区：
文献类型：
--
作者：
R. Poliquin
1977年，海蒂·阿图什（Hedy Attouch）证明了一列（闭的真）凸函数依上图象收敛到一个凸函数，当且仅当次微分的图象（在莫斯科收敛意义下）收敛到极限函数的次微分，并且（大致来说）存在一个确定积分常数的条件。我们表明，如果考虑的是一个闭的真凸函数与一个二次连续可微映射的复合函数（此外还施加一个约束规格条件），该定理仍然成立。
In 1977, Hedy Attouch established that a sequence of (closed proper) convex functions epi-converges to a convex function if and only if the graphs of the subdierentials converge (in the Mosco sense) to the subdifferential of the limiting function and (roughly speaking) there is a condition that fixes the constant of integration. We show that the theorem is valid if instead one considers functions that are the composition of a closed proper convex function with a twice continuously differentiable mapping (in addition a constraint qualification is imposed)