Complementarity-Gap-Driven Adaptive Sequential Convex Programming for Reentry Trajectory Optimization

Abstract

To address the issue that existing penalty weight update strategies in the augmented Lagrangian multiplier method are disconnected from the optimality conditions and remain relatively sensitive to initial parameters, this paper proposes a complementarity-gap-driven adaptive sequential convex programming algorithm. The algorithm directly incorporates the complementarity slackness information from the KKT conditions into the parameter update laws. The defined complementarity slackness ratio and complementarity gap respectively measure the deviation of the current penalty intensity from the ideal multiplier level and the degree of departure from the complementarity slackness condition. Based on these two quantities, a bidirectional smooth update law for the penalty weight and a normalized gap update law for the multiplier are designed, which decouple the multiplier growth from the current multiplier magnitude. On this basis, a complete theoretical convergence framework is established, in which the monotonic bounded convergence of the Lagrange multiplier and the convergence of the slack variables and the complementarity gap are rigorously proved, and a conditional convergence theorem is given. Taking the reentry trajectory planning problem of a gliding vehicle as an example, numerical simulations are conducted with the initial penalty weight spanning five orders of magnitude. Simulation results demonstrate that the proposed algorithm converges rapidly and stably to the optimal solution satisfying the accuracy requirements under different initial weights, with the terminal position error stabilizing at 0.4–0.5 km, exhibiting favorable convergence accuracy. In addition, the stable convergence exhibited by the complementarity gap and the slackness radius validates the effectiveness and robustness of the complementarity-gap-driven adaptive update mechanism.