Barrier function in the Lagrangian dual method for solving
multi-stage stochastic nonlinear programs
This paper presents an algorithm for solving multi-stage stochastic
nonlinear programs. The algorithm is based on the Lagrangian dual
method, which relaxes the nonanticipative constraints, and the barrier
function method, which enhances the smoothness of the dual objective
function so that the Newton search direction and even higher-order
search directions can be use. The algorithm is shown to be of globally
linear convergence and of polynomial-time complexity.
Working paper, Dept of Math., National University of
Singapore, Singapore, 1998.