论文标题
解决由多项式优化引起的聚类的低级别半决赛程序
Solving clustered low-rank semidefinite programs arising from polynomial optimization
论文作者
论文摘要
我们研究了一种原始的双重内部点方法，专门针对需要高精度数字的簇的低级别半额定程序，该方法是由某些多元多项式（矩阵）程序引起的。我们考虑采样和对称性还原的相互作用以及贪婪的方法，以获得数值良好的碱基和采样点。我们将其应用于接吻数问题的三点边界的计算，为此我们显示了显着的加速。这允许计算改进的接吻数量界限，$ 11 $至$ 23 $。该方法对于不良数值调节问题的问题表现良好，我们通过针对二进制球体包装问题进行的新计算显示。
We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polynomial (matrix) programs through sums-of-squares characterizations and sampling. We consider the interplay of sampling and symmetry reduction as well as a greedy method to obtain numerically good bases and sample points. We apply this to the computation of three-point bounds for the kissing number problem, for which we show a significant speedup. This allows for the computation of improved kissing number bounds in dimensions $11$ through $23$. The approach performs well for problems with bad numerical conditioning, which we show through new computations for the binary sphere packing problem.
