A Boosted-DCA with Power-Sum-DC Decomposition for Linearly Constrained Polynomial Program
2022
academicJournal
Zugriff:
In this paper, we introduce a difference-of-convex (DC) decomposition for polynomials based on power-sum representation, which can be established by solving a sparse linear system. A boosted DCA with exact line search (BDCAe) is proposed to solve the DC formulation of the linearly constrained polynomial program. We show that the exact line search is equivalent to finding roots of a unary polynomial in an interval, which has a closed-form solution in many applications. The subsequential convergence of BDCAe to a critical point is proved, and the convergence rate under Kurdyka-Lojasiewicz property is established. Moreover, a fast dual proximal gradient (FDPG) method is applied to efficiently solve the resulting convex subproblems. Numerical experiments on the Mean-Variance-Skewness-Kurtosis (MVSK) portfolio optimization model via BDCAe, DCA, BDCA with Armijo line search, as well as FMINCON and FILTERSD solvers are reported, which demonstrates good performance of BDCAe. ; Comment: 26 pages, 3 figures
Titel: |
A Boosted-DCA with Power-Sum-DC Decomposition for Linearly Constrained Polynomial Program
|
---|---|
Autor/in / Beteiligte Person: | Zhang, Hu ; Niu, Yi-Shuai |
Link: | |
Veröffentlichung: | 2022 |
Medientyp: | academicJournal |
Schlagwort: |
|
Sonstiges: |
|