# Computing B-Stationary Points of Nonsmooth DC Programs

arXiv: https://arxiv.org/abs/1511.01796 · HTML: https://mlsanity.com/paper/1511.01796/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2015.

## Built on by (most cited first, 12 of 12)

- [Large-scale Optimization of Partial AUC in a Range of False Positive Rates](https://mlsanity.com/paper/2203.01505/) (2022)
- [Non-geodesically-convex optimization in the Wasserstein space](https://mlsanity.com/paper/2406.00502/) (2024)
- [Coordinate Descent Methods for DC Minimization: Optimality Conditions and Global Convergence](https://mlsanity.com/paper/2109.04228/) (2021)
- [Coordinate Descent Methods for Fractional Minimization](https://mlsanity.com/paper/2201.12691/) (2022)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [Learning Robust Treatment Rules for Censored Data](https://mlsanity.com/paper/2408.09155/) (2024)
- [A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2502.17602/) (2025)
- [A Refined Inertial DC Algorithm for DC Programming](https://mlsanity.com/paper/2104.14750/) (2021)
- [An inexact LPA for DC composite optimization and application to matrix completions with outliers](https://mlsanity.com/paper/2303.16822/) (2023)
- [RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs](https://mlsanity.com/paper/2605.23550/) (2026)
- [MoSSP: A Momentum-Based Single-Loop Stochastic Penalty Method for Nonconvex Constrained DC-Regularized Optimization](https://mlsanity.com/paper/2605.29635/) (2026)
- [Online Optimization of Difference-of-Convex Compositions with Smooth Mappings](https://mlsanity.com/paper/2607.19553/) (2026)

## Abstract (arXiv)

Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc) minimization problem. The contributions of this paper are: (i) clarify several kinds of stationary solutions and their relations; (ii) develop and establish the convergence of a novel algorithm for computing a d-stationary solution of a problem with a convex feasible set that is arguably the sharpest kind among the various stationary solutions; (iii) extend the algorithm in several directions including: a randomized choice of the subproblems that could help the practical convergence of the algorithm, a distributed penalty approach for problems whose objective functions are sums of dc functions, and problems with a specially structured (nonconvex) dc constraint. For the latter class of problems, a pointwise Slater constraint qualification is introduced that facilitates the verification and computation of a B(ouligand)-stationary point.