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.