  This paper proposes a new algorithm that solves non-convex optimal control
problems with a theoretical guarantee for global convergence to a feasible
local solution of the original problem. The proposed algorithm extends the
recently proposed successive convexification (SCvx) algorithm by addressing one
of its key limitations, that is, the converged solution is not guaranteed to be
feasible to the original non-convex problem. The main idea behind the proposed
algorithm is to incorporate the SCvx-based iteration into an algorithmic
framework based on the augmented Lagrangian method to enable the feasibility
guarantee while retaining favorable properties of SCvx. Unlike the original
SCvx, this approach iterates on both of the optimization variables and the
Lagrange multipliers, which facilitates the feasibility guarantee as well as
efficient convergence, in a spirit similar to the alternating direction method
of multipliers (ADMM) for large-scale convex programming. Convergence analysis
shows the proposed algorithm's strong global convergence to a feasible local
optimum of the original problem and its convergence rate. These theoretical
results are demonstrated via numerical examples with comparison against the
original SCvx algorithm.
