  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.
