# Self-adaptive ADMM for semi-strongly convex problems

arXiv: https://arxiv.org/abs/2310.00376 · HTML: https://mlsanity.com/paper/2310.00376/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2023.

## Built on by (most cited first, 2 of 2)

- [Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2404.09438/) (2024)
- [Alternating minimization for square root principal component pursuit](https://mlsanity.com/paper/2501.00471/) (2024)

## Abstract (arXiv)

In this paper, we develop a self-adaptive ADMM that updates the penalty parameter 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/k^2), 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 subproblem 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.