A superlinearly convergent algorithm for large scale multi-stage stochastic nonlinear programming

This paper presents an algorithm for solving a class of large scale nonlinear programming problem which is originally derived from the multi-stage stochastic convex nonlinear programming. Using the Lagrangian-dual method and the Moreau-Yosida regularization, the primal problem is neatly transformed into a smooth convex problem. By introducing a self-concordant barrier function, an approximate generalized Newton method is then designed to solve the problem. The algorithm is shown to be of superlinear convergence. Some numerical results are presented to demonstrate the viability of the proposed method.