Successive Convexification with Feasibility Guarantee via Augmented Lagrangian for Non-Convex Optimal Control Problems

This paper proposes an 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 to address its key limitation: lack of feasibility guarantee to the original non-convex problem. The main idea of the proposed algorithm is to incorporate the SCvx 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, our 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). 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.