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In this paper, we introduce a difference-of-convex (DC) decomposition forpolynomials based on power-sum representation, which can be established bysolving a sparse linear system. A boosted DCA with exact line search (BDCAe) isproposed to solve the DC formulation of the linearly constrained polynomialprogram. We show that the exact line search is equivalent to finding roots of aunary polynomial in an interval, which has a closed-form solution in manyapplications. The subsequential convergence of BDCAe to a critical point isproved, and the convergence rate under Kurdyka-Lojasiewicz property isestablished. Moreover, a fast dual proximal gradient (FDPG) method is appliedto efficiently solve the resulting convex subproblems. Numerical experiments onthe Mean-Variance-Skewness-Kurtosis (MVSK) portfolio optimization model viaBDCAe, DCA, BDCA with Armijo line search, as well as FMINCON and FILTERSDsolvers are reported, which demonstrates good performance of BDCAe.

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