论文标题
克拉克的切线锥，亚级别，最佳条件和无穷大的Lipschitzness
Clarke's tangent cones, subgradients, optimality conditions and the Lipschitzness at infinity
论文作者
论文摘要
我们首先研究Clarke在Infinity的切线锥到$ \ Mathbb {r}^n。$的无界子集，我们证明这些锥体是封闭的凸面并显示了其内部的特征。然后，我们在$ \ mathbb {r}^n $上研究无穷大的亚级别的扩展实际价值函数，并在无穷大的优化问题上得出了必要的最佳条件。我们还提供了许多规则，用于计算无穷大的亚级别的计算，并为LIPSCHITZ连续性提供了无穷大的较低半连续功能的一些特征。
We first study Clarke's tangent cones at infinity to unbounded subsets of $\mathbb{R}^n.$ We prove that these cones are closed convex and show a characterization of their interiors. We then study subgradients at infinity for extended real value functions on $\mathbb{R}^n$ and derive necessary optimality conditions at infinity for optimization problems. We also give a number of rules for the computing of subgradients at infinity and provide some characterizations of the Lipschitz continuity at infinity for lower semi-continuous functions.
