Descent Property in Sequential Second-Order Cone Programming for Nonlinear Trajectory Optimization

Sequential second-order cone programming (SSOCP) is commonly used in aerospace applications for solving nonlinear trajectory optimization problems. The SSOCP possesses good real-time performance. However, one long-standing challenge is its unguaranteed convergence. In this paper, we theoretically analyze the descent property of the L1 penalty function in the SSOCP. Using Karush-Kuhn-Tucker conditions, we obtain two important theoretical results: 1) the L1 penalty function of the original nonlinear problem always descends along the iteration direction; 2) a sufficiently small trust region can decrease the L1 penalty function. Based on these two results, we design an improved trust region shrinking algorithm with theoretically guaranteed convergence. In numerical simulations, we verify the proposed algorithm using a reentry trajectory optimization problem.