关于通过广义导数图中的子空间的多值函数的（局部）分析
On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives
摘要：
本文讨论了映射的一个综合理论，它的局部行为可以用包含在两个（原始和对偶）广义导数的图中的线性子空间来描述。这类映射包括图形上的利普希茨映射，因而也包括一些在最优化和平衡问题中经常出现的多值函数。发展的理论利用自己的广义导数，为我们提供了一些微积分规则，并揭示了一些有趣的连接。特别是，它使我们能够构建一个修改的半光滑 * 牛顿方法与改进的收敛性能，并推导出一个推广的克拉克的反函数定理的多功能与新的有效的强度量（子）的正则性和倾斜稳定性。
英文摘要：
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the graphically Lipschitzian mappings and thus a number of multifunctions, frequently arising in optimization and equilibrium problems. The developed theory makes use of own generalized derivatives, provides us with some calculus rules and reveals a number of interesting connections. In particular, it enables us to construct a modification of the semismooth* Newton method with improved convergence properties and to derive a generalization of Clarke's Inverse Function Theorem to multifunctions together with new efficient characterizations of strong metric (sub)regularity and tilt stability.
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