# Convergence Analysis of a Proximal Point Algorithm for Minimizing Differences of Functions

arXiv: https://arxiv.org/abs/1504.08079 · HTML: https://mlsanity.com/paper/1504.08079/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2015.

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

- [Large-scale Optimization of Partial AUC in a Range of False Positive Rates](https://mlsanity.com/paper/2203.01505/) (2022)
- [An inexact LPA for DC composite optimization and application to matrix completions with outliers](https://mlsanity.com/paper/2303.16822/) (2023)

## Abstract (arXiv)

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka - L ojasiewicz property.