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

Abstract

This paper presents an algorithm for solving a class of large scale nonlinear programming which is originally derived from the multi-stage stochastic convex nonlinear programming. With the Lagrangian-dual method and the Moreau-Yosida regularization, the primal problem is transformed into a smooth convex problem. By introducing a self-concordant barrier function, an approximate generalized Newton method is designed in this paper. The algorithm is shown to be of superlinear convergence. At last, some preliminary numerical results are provided.