SCvx-Frank-Wolfe Algorithm

Convex optimization algorithms are increasingly used in embedded trajectory planning for safety-critical systems, requiring verification to meet safety standards. Previous research has shown that formal verification methods can be applied to convex solvers for linear problems. This paper explores a specific implementation of the successive convexification approach for trajectory planning using linear programming. We focus on a new implementation of the successive convexification algorithm based on the Frank-Wolfe method (FW-SCVX), aiming at demonstrating that it maintains algorithm performance and is suitable for embedded systems. We also analyze the convergence of the FW-SCVX algorithm and provide numerical evaluations to support our proposal. This work contributes to the formal verification of advanced trajectory planning algorithms in safety-critical embedded systems.