  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.
