In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic differential equations introduced by Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169--198). After giving a brief review of the cubature theory on Wiener space, we show that a cubature formula of general dimension and degree can be obtained through a Monte Carlo sampling and linear programming. This paper also includes an extension of stochastic Tchakaloff's theorem, which technically yields the proof of our primary result.

翻译：在本文中,我们研究数学优化应用于构建维纳空间的幼稚公式,这是里昂斯和维克托尔(维纳空间古巴,Proc. R. Soc. Lond. A 460, 169-198)引入的软性切分方程式近似法,这是利昂斯和维克托尔(维纳空间古巴,Proc. R. Soc. Lond. A 460, 169-198)引入的一种微弱的近似法。在简要审查了维纳空间的幼稚理论之后,我们发现,可以通过蒙特卡洛取样和线性编程获得一个通用和学位的幼稚公式。本文还包含一个从技术上证明我们主要结果的“技术”Tchakaloff理论的延伸。