  We introduce a GPU-accelerated Monte Carlo framework for nonconvex,
free-final-time trajectory optimization problems. This framework makes use of
the prox-linear method, which belongs to the larger family of sequential convex
programming (SCP) algorithms, in conjunction with a constraint reformulation
that guarantees inter-sample constraint satisfaction. Key features of this
framework are: (1) continuous-time constraint satisfaction; (2) a
matrix-inverse-free solution method; (3) the use of the proportional-integral
projected gradient (PIPG) method, a first-order convex optimization solver,
customized to the convex subproblem at hand; and, (4) an end-to-end,
library-free implementation of the algorithm. We demonstrate this GPU-based
framework on the 6-DoF powered-descent guidance problem, and show that it is
faster than an equivalent serial CPU implementation for Monte Carlo simulations
with over 1000 runs. To the best of our knowledge, this is the first GPU-based
implementation of a general-purpose nonconvex trajectory optimization solver.
