@article{TangToh2023,
  author    = {Tang, Tianyun and Toh, Kim-Chuan},
  title     = {Self-adaptive ADMM for semi-strongly convex problems},
  journal   = {Mathematical Programming Computation},
  volume    = {16},
  number    = {1},
  publisher = {Springer Science and Business Media LLC},
  issn      = {1867-2949},
  doi       = {10.1007/s12532-023-00250-8},
  pages     = {113 -- 150},
  year      = {2023},
  abstract  = {In this paper, we develop a self-adaptive ADMM that updates the penalty parame- ter adaptively. When one part of the objective function is strongly convex i.e., the problem is semi-strongly convex, our algorithm can update the penalty parameter adaptively with guaranteed convergence. We establish various types of convergence results including accelerated convergence rate of O(1/k2), linear convergence and convergence of iteration points. This enhances various previous results because we allow the penalty parameter to change adaptively. We also develop a partial proximal point method with the subproblems being solved by our adaptive ADMM. This enables us to solve problems without semi-strongly convex property. Numerical experiments are conducted to demonstrate the high efficiency and robustness of our method.},
  language  = {en}
}