论文标题
正常锥体的替代表示与超级函数的域和细分微积分的域
Alternative representations of the normal cone to the domain of supremum functions and subdifferential calculus
论文作者
论文摘要
本文的第一部分提供了正常锥体的新特征，该特征是任意凸函数家族至上的有效领域。这些结果在第二部分中应用，以提供最高函数的亚差异的新公式，这些函数在参考点上同时使用活动和非活动函数。这些特征仅涉及数据功能，即从一侧进行的活动功能，以及非活动函数乘以一些适当的参数。与文献中的先前作品相反，我们的亚差异表征的主要特征是，正常锥到上皮的有效域（或该域的有限维截面）没有出现。在本文末尾建立了一种新型的凸优化最佳条件。
The first part of the paper provides new characterizations of the normal cone to the effective domain of the supremum of an arbitrary family of convex functions. These results are applied in the second part to give new formulas for the subdifferential of the supremum function, which use both the active and nonactive functions at the reference point. Only the data functions are involved in these characterizations, the active ones from one side, together with the nonactive functions multiplied by some appropriate parameters. In contrast with previous works in the literature, the main feature of our subdifferential characterization is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of this domain) does not appear. A new type of optimality conditions for convex optimization is established at the end of the paper.
