Formal augmented Newtonian projection methods for continuous-time optimal control problems

Certain continuous-time optimal control problems with smooth objective functions, simple convex admissible control input sets, and terminal state equality constraints can be treated efficiently with formal Newtonian projection schemes and augmented Lagrangian techniques. The required gradients, Newtonian scaling operators, and second-order multiplier update formulas are determined by systems of forward and backward initial value problems for differential equations derived from a Hamiltonian function. In practice, the latter problems are solved approximately with finite-difference methods at a cost of O(k) flops per iteration, where k is the number of subintervals in the finite-difference grid. Substantial portions of the work can be organized for parallel computation