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 [Formula: see text] penalty function in the SSOCP. Using Karush–Kuhn–Tucker conditions, we obtain two important theoretical results: 1) the [Formula: see text] penalty function of the original nonlinear problem always descends along the iteration direction; 2) a sufficiently small trust region can decrease the [Formula: see text] 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.