Newton's method for quadratic stochastic programs with recourse (Q1900750)

A Newton-like method is used to solve a system of nonsmooth equations obtained from the Kuhn-Tucker conditions for the nonlinear convex programming problem which approximate a two-stage quadratic stochastic program with fixed recourse. It is proved that the proposed method realizes global convergence and superlinear local convergence, and is more general than previous methods which were developed for box-diagonal and fully quadratic stochastic programs. Finally, numerical results obtained both with the proposed algorithm for different starting points and with the variants of the algorithm that use Monte Carlo rules and lattice rules for numerical integration are given.