论文标题
凸随机优化的双重解决方案
Dual solutions in convex stochastic optimization
论文作者
论文摘要
本文研究了一般凸随机优化问题的二元性和最佳条件。主要结果为缺乏二元性差距和在随机变量的局部凸空间中存在双重溶液提供了足够的条件。它尤其暗示着方案的最佳条件的必要性，这些条件背后是运营研究，随机最佳控制和金融数学的许多基本结果。我们的分析建立在随机变量的Fréchet空间理论上，其拓扑二可以通过随机变量的另一个空间的直接总和和一个奇异函数的空间来识别。通过为几个更具体的问题类得出足够且必要的最佳条件来说明结果。我们获得了早期模型的显着扩展，例如随机最佳控制，投资组合优化和数学编程。
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental results in operations research, stochastic optimal control and financial mathematics. Our analysis builds on the theory of Fréchet spaces of random variables whose topological dual can be identified with the direct sum of another space of random variables and a space of singular functionals. The results are illustrated by deriving sufficient and necessary optimality conditions for several more specific problem classes. We obtain significant extensions to earlier models e.g.\ on stochastic optimal control, portfolio optimization and mathematical programming.
