A full-space quasi-lagrange-Newton-krylov algorithm for trajectory optimization problems

The objectives of this work are to study and to apply the full-space quasi-Lagrange-Newton-Krylov (FQLNK) algorithm for solving trajectory optimization problems arising from aerospace industrial applications. As its name suggests, in this algorithm we first convert the constrained optimization problem into an unconstrained one by introducing the augmented Lagrangian parameters. The next step is to find the optimal candidate solution by solving the Karush-Kuhn-Tucker (KKT) system with a Newton-Krylov method. To reduce the computational cost of constructing the KKT system, we employ the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to build an approximation of the (1,1) subblock of the KKT matrix, which is the most expensive part of the overall computation. The BFGS-based FQLNK algorithm exhibits a superior speedup compared to some of the alternatives. We demonstrate our FQLNK algorithm to be a practical approach for designing an optimal trajectory of a launch vehicle in space missions.