PANOC

Main solver used for the box-constrained inner problem.

• Lorenzo Stella, Andreas Themelis, Pantelis Sopasakis, and Panagiotis Patrinos, “A Simple and Efficient Algorithm for Nonlinear Model Predictive Control,” 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, Australia, 2017, pp. 1939─1944.
  Original paper introducing the PANOC algorithm.
• Pantelis Sopasakis, Emil Fresk, and Panagiotis Patrinos, “OpEn: Code Generation for Embedded Nonconvex Optimization,” 21^st IFAC World Congress: Proceedings, Berlin, Germany, 2020.
  A Rust implementation of PANOC with ALM and penalty methods, with Python code generation. Website.

Anderson acceleration

Acceleration for the fixed-point projected gradient method.

• Donald G.M. Anderson, “Iterative procedures for nonlinear integral equations”. Journal of the Association for Computing Machinery, Vol. 12, No. 4, pp. 547─560, 1965.
  Original paper introducing the idea of Anderson acceleration, not that relevant for the algorithm we implemented.
• Donald G.M. Anderson, Comments on “Anderson Acceleration, Mixing and Extrapolation,” Numerical Algorithms, Vol. 80, No. 1: pp. 135─234, 2017.
  Long but interesting discussion of Anderson acceleration by Anderson himself, also discussing other publications on the topic.
• Homer F. Walker and Peng Ni, “Anderson acceleration for fixed-point iterations,” SIAM Journal on Numerical Analysis, Vol. 49, No. 4, pp. 1715─1735, 2011.
  Anderson acceleration applied to fixed-point iteration, covers the math used for the implementation of our algorithm.
  PDF with pseudocode and Mᴀᴛʟᴀʙ implementation: https://users.wpi.edu/~walker/Papers/anderson_accn_algs_imps.pdf
• Vien V. Mai and Mikael Johansson, “Anderson Acceleration of Proximal Gradient Methods,” arXiv:1910.08590, 2020.
  Guarded Anderson accelerated proximal gradient algorithm. A slightly modified version is used in our code.
• J.W. Daniel, W.B. Gragg, L. Kaufman and G.W. Stewart, “Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization,” Mathematics of computation, Vol. 30, No. 136, pp. 772─795, 1976.
  Algorithm for incrementally updating the QR factorization when columns are added or removed.
• Christian Bischof, Ping Tak Peter Tang, “Robust Incremental Condition Estimation,” SIAM Journal on Matrix Analysis and Applications, Vol. 11, No. 2, pp. 312─322, 1990.
  Another, newer (unpublished?) version: https://www.osti.gov/biblio/10133022-Zz8cvq/native
  Better quality PDF: http://www.netlib.org/lapack/lawnspdf/lawn33.pdf