# A Boosted-DCA with Power-Sum-DC Decomposition for Linearly Constrained Polynomial Programs

arXiv: https://arxiv.org/abs/2205.02571 · HTML: https://mlsanity.com/paper/2205.02571/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2022.

## Built on by (most cited first, 3 of 3)

- [Non-geodesically-convex optimization in the Wasserstein space](https://mlsanity.com/paper/2406.00502/) (2024)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [An Improved Boosted DC Algorithm for Nonsmooth Functions with Applications in Image Recovery](https://mlsanity.com/paper/2602.04237/) (2026)

## Abstract (arXiv)

This paper proposes a novel Difference-of-Convex (DC) decomposition for polynomials using a power-sum representation, achieved by solving a sparse linear system. We introduce the Boosted DCA with Exact Line Search (BDCAe) for addressing linearly constrained polynomial programs within the DC framework. Notably, we demonstrate that the exact line search equates to determining the roots of a univariate polynomial in an interval, with coefficients being computed explicitly based on the power-sum DC decompositions. The subsequential convergence of BDCAe to critical points is proven, and its convergence rate under the Kurdyka-Lojasiewicz property is established. To efficiently tackle the convex subproblems, we integrate the Fast Dual Proximal Gradient (FDPG) method by exploiting the separable block structure of the power-sum DC decompositions. We validate our approach through numerical experiments on the Mean-Variance-Skewness-Kurtosis (MVSK) portfolio optimization model and box-constrained polynomial optimization problems. Comparative analysis of BDCAe against DCA, BDCA with Armijo line search, UDCA, and UBDCA with projective DC decomposition, alongside standard nonlinear optimization solvers FMINCON and FILTERSD, substantiates the efficiency of our proposed approach.