Augmented Lagrangian Method
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A constraint-handling method that augments the objective function with both Lagrange multiplier terms and a quadratic penalty term. In HDDP, terminal constraints ψ=0 are adjoined via multipliers λ and a penalty matrix Σ as φ+λᵀψ+ψᵀΣψ. Multipliers are updated each iteration to steer the trajectory toward feasibility; the penalty provides additional discouragement of constraint violations for stability. Compared to pure penalty methods, the augmented Lagrangian converges to the exact solution without requiring the penalty weight to grow unboundedly.
Application Value
在轨道动力学数值仿真中，该方法用于提高计算精度和效率. 通过合理的离散化策略，可以在保证数值稳定性的同时大幅减少计算量.
Related Concepts
- Hill 模型（Hill Model）
- 惯性坐标系固定编队（Formation Fixed Relative to Inertial Frame）
- 受摄Lambert问题（Perturbational Lambert Problem）
- 探测器定位（Probe Targeting）
References
- Lantoine & Russell 2012, JOTA Part 1 & 2; Aziz et al. 2019, JGCD