最佳数据拟合：矩方法
Optimal data fitting: a moment approach
摘要：
我们提出了两个问题的矩松弛，分离和覆盖问题的半代数集所产生的多项式的d次。我们证明了：（a）当矩阶r增加时，松弛解的最优值收敛到原问题的最优值;（b）对原问题进行一些小的扰动后，当r=d时，可以达到收敛。我们还提供了一个实用的迭代算法，计算上易于处理的大型数据集，并提出令人鼓舞的计算结果。
英文摘要：
We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order r increases and (b) after performing some small perturbation of the original problem, convergence can be achieved with r=d. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.
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