ADMM for quadratic equations

Lecture notes

• Stanford (Boyd/Duchi): EE 364B
• UCLA (Vandenberghe): EE 236C
• UCLA (Yin): Math 273a

Source code

• Wirtinger flow
• Truncated Wirtinger flow

For applications to phase retrieval, see recent papers by Albert Fannjiang.

Classics

• Eckstein, Bertsekas: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators (doi)
  • Proves that DR (and hence ADMM) is a special case of the proximal point algorithm
• Rockafellar: Monotone operators and the proximal point algorithm (doi)
  • Key paper on PPA, cited by Boyd re: \(\rho \to \infty\)

Borwein’s papers on DRS for nonconvex optimization:

• 2015: Global behavior of the Douglas-Rachford method for a nonconvex feasibility problem (pdf)
• 2013: Recent results on Douglas-Rachford methods for combinatorial optimization problems (arxiv)
• 2012: Global convergence of a non-convex Douglas-Rachford iteration (pdf, slides)
• 2009: The Douglas-Rachford algorithm in the absence of convexity (pdf)

Nonconvex ADMM

• Hong, Luo, Razaviyan: Convergence analysis of ADMM for a family of nonconvex problems (arxiv)
  • Via Stack Exchange but contra the answer, it doesn’t apply to biconvex problems
• Wang, Yin, Zeng: Global convergence of ADMM in nonconvex nonsmooth optimization (online )