PIPG: Proportional-Integral Projected Gradient Algorithm for Trajectory Optimization

• ./PIPG contains the implementaion of PIPG for conic optimization as described in Yu et al. 2022. The two examples in the paper are formulated in ex1_problem_data.jl and ex2_problem_data.jl. The simulations are carried out in the corresponding notebooks ex1_problem_solve.jl and ex2_problem_solve.jl.
• PIPGeq_demo.ipynb implements an earlier version of PIPG (called PIPGeq) described in Yu et al. 2020
• ./xPIPG contains the implementation of the extrapolated PIPG for infeasibility detection described in Yu et al. 2022.

Citations

Conic optimization solver PIPGeq specialized to affine equality constraint and convex set constraints which allow efficient projections.

@article{pipgeq,
  author={Yu, Yue and Elango, Purnanand and A\c{c}\i kme\c{s}e, Beh\c{c}et},
  journal={IEEE Control Systems Letters}, 
  title={Proportional-Integral Projected Gradient Method for Model Predictive Control}, 
  year={2021},
  volume={5},
  number={6},
  pages={2174-2179},
  doi={10.1109/LCSYS.2020.3044977}
}

Conic optimization solver PIPG which can handle general conic constraints and convex set constraints which allow efficient projections.

@article{pipg,
  author = {Yue Yu and Purnanand Elango and Ufuk Topcu and Beh\c{c}et~A\c{c}\i kme\c{s}e},
  title = {Proportional–integral projected gradient method for conic optimization},
  journal = {Automatica},
  volume = {142},
  pages = {110359},
  year = {2022},
  issn = {0005-1098},
  doi = {https://doi.org/10.1016/j.automatica.2022.110359},
  url = {https://www.sciencedirect.com/science/article/pii/S0005109822002096}
}

Infeasibility detection using PIPG.

@misc{pipg-infeas,
  author = {Yu, Yue and Topcu, Ufuk},    
  title = {Proportional-Integral Projected Gradient Method for Infeasibility Detection in Conic Optimization},
  publisher = {arXiv},  
  year = {2021},
  doi = {10.48550/ARXIV.2109.02756},  
  url = {https://arxiv.org/abs/2109.02756}
}

Extrapolated PIPG.

@article{xpipg,
  author = {Yu, Yue and Elango, Purnanand and A\c{c}\i kme\c{s}e, Beh\c{c}et and Topcu, Ufuk}, 
  title = {Extrapolated Proportional-Integral Projected Gradient Method for Conic Optimization},
  journal = {IEEE Control Systems Letters (accepted)},
  year = {2022},
  volume={},
  number={},
  pages={},
  doi={10.48550/ARXIV.2203.04188},
  url = {https://arxiv.org/abs/2203.04188}
}

Customized PIPG for real-time powered-descent guidance.

@inproceedings{pipg-pdg,
  author={Elango, Purnanand and Kamath, Abhinav G. and Yu, Yue and Carson III, John M. and Mesbahi, Mehran and A\c{c}\i kme\c{s}e, Beh\c{c}et}, 
  title={A Customized First-Order Solver for Real-Time Powered-Descent Guidance}, 
  booktitle={AIAA SciTech 2022 Forum}, 
  publisher={American Institute of Aeronautics and Astronautics}, 
  year={2022}, 
  month={Jan},  
  doi={10.2514/6.2022-0951}, 
  url={https://arc.aiaa.org/doi/abs/10.2514/6.2022-0951}
}