  This paper presents a convex programming approach to the optimization of a
multistage launch vehicle ascent trajectory, from the liftoff to the payload
injection into the target orbit, taking into account multiple nonconvex
constraints, such as the maximum heat flux after fairing jettisoning and the
splash-down of the burned-out stages. Lossless and successive convexification
are employed to convert the problem into a sequence of convex subproblems.
Virtual controls and buffer zones are included to ensure the recursive
feasibility of the process and a state-of-the-art method for updating the
reference solution is implemented to filter out undesired phenomena that may
hinder convergence. A hp pseudospectral discretization scheme is used to
accurately capture the complex ascent and return dynamics with a limited
computational effort. The convergence properties, computational efficiency, and
robustness of the algorithm are discussed on the basis of numerical results.
The ascent of the VEGA launch vehicle toward a polar orbit is used as case
study to discuss the interaction between the heat flux and splash-down
constraints. Finally, a sensitivity analysis of the launch vehicle carrying
capacity to different splash-down locations is presented.
