# Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems

arXiv: https://arxiv.org/abs/1911.04334 · HTML: https://mlsanity.com/paper/1911.04334/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2019.

## 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)
- [Learning Robust Treatment Rules for Censored Data](https://mlsanity.com/paper/2408.09155/) (2024)

## Abstract (arXiv)

The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect to a probability distribution. This class of nonsmooth and nonconvex stochastic optimization problems plays a central role in many practical applications. Although there are many contributions in the context of convex and/or smooth stochastic optimization, algorithms dealing with nonconvex and nonsmooth programs remain rare. In deterministic optimization literature, the DC Algorithm (DCA) is recognized to be one of the few algorithms to solve effectively nonconvex and nonsmooth optimization problems. The main purpose of this paper is to present some new stochastic DCAs for solving stochastic DC programs. The convergence analysis of the proposed algorithms is carefully studied, and numerical experiments are conducted to justify the algorithms' behaviors.