# An adaptive proximal point algorithm framework and application to large-scale optimization

arXiv: https://arxiv.org/abs/2008.08784 · HTML: https://mlsanity.com/paper/2008.08784/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Complexity of Inexact Proximal Point Algorithm for minimizing convex functions with Holderian Growth](https://mlsanity.com/paper/2108.04482/) (2021)

## Abstract (arXiv)

We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition parameter. We propose an adaptive generalized proximal point algorithm (AGPPA), which adaptively updates the proximal regularization parameters based on some implementable criteria. We show that AGPPA achieves linear convergence without any knowledge of the error bound condition parameter, and the rate only differs from the optimal one by a logarithm term. We apply AGPPA on convex minimization problem and analyze the iteration complexity bound of the resulting algorithm. Our framework and the complexity results apply to arbitrary linearly convergent inner solver and allows a hybrid with any locally fast convergent method. We illustrate the performance of AGPPA by applying it to solve large-scale linear programming (LP) problem. The resulting complexity bound has a weaker dependence on the Hoffman constant and scales with the dimension better than linearized ADMM. In numerical experiments, our algorithm demonstrates improved performance in obtaining solution of medium accuracy on large-scale LP problem.