Newtonʹs method for quadratic stochastic programs with recourse

Quadratic stochastic programs (QSP) with recourse can be formulated as nonlinear convex programming problems. By attaching a Lagrange multiplier vector to the nonlinear convex program, a QSP is written as a system of nonsmooth equations. A Newton-like method for solving the QSP is proposed and global convergence and local super-linear convergence of the method are established. The current method is more general than previous methods which were developed for box-diagonal and fully quadratic QSP. Numerical experiments are given to demonstrate the efficiency of the algorithm, and to compare the use of Monte-Carlo rules and lattice rules for multiple integration in the algorithm.