论文标题
最佳价值函数的规律性特性的粘度解决方案方法
A viscosity solution approach to regularity properties of the optimal value function
论文作者
论文摘要
在本文中，我们分析了通过粘度解决方案理论与一般参数优化问题相关的最佳值函数$ V $。新颖性是，我们通过表明它是一组一阶方程的粘度解决方案来获得$ V $的规律性属性。结果，在Banach空间中，我们为$ V $的本地和全球Lipschitz物业提供了足够的条件。在有限的维度下，我们还通过比较原理得出了最佳的条件。最后，我们研究了粘度和Clarke广义解决方案之间的关系，以获得欧几里得空间中$ V $的进一步可不同性能。
In this paper we analyze the optimal value function $v$ associated to a general parametric optimization problems via the theory of viscosity solutions. The novelty is that we obtain regularity properties of $v$ by showing that it is a viscosity solution to a set of first-order equations. As a consequence, in Banach spaces, we provide sufficient conditions for local and global Lipschitz properties of $v$. We also derive, in finite dimensions, conditions for optimality through a comparison principle. Finally, we study the relationship between viscosity and Clarke generalized solutions to get further differentiability properties of $v$ in Euclidean spaces.
