Second-Order Multiplier Update Calculations for Optimal Control Problems and Related Large Scale Nonlinear Programs

A second-order multiplier update rule is applied to K-stage discrete-time optimal control problems with control and state variable constraints. Each update entails the assembly and solution of sparse block-banded equilibrium equations. Several direct elimination solution techniques are considered, and it is shown that the updates can always be calculated in $O( K )$ flops. Part of the analysis applies not only to control problems, but also to other similarly structured large scale nonlinear programs with equality and inequality constraints.