Intrinsic volumes of symmetric cones and applications in convex programming
Intrinsic volumes of symmetric cones and applications in convex programming
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DOI：
10.1007/s10107-013-0740-2
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发表时间：
2015-02
影响因子：
2.7
通讯作者：
Dennis Amelunxen;Peter Bürgisser
中科院分区：
文献类型：
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作者：
Dennis Amelunxen;Peter Bürgisser
我们表示的随机（标准高斯）的凸锥程序的实例的解决方案的概率分布的内在卷和曲率措施的参考锥。然后，我们计算的内在体积的锥的半正定矩阵的真实的数字，在复数，并在四元数的积分相关的梅塔的积分。特别是，我们得到了一个封闭的公式的概率，一个随机（标准高斯）半定规划的解决方案有一定的秩。
We express the probability distribution of the solution of a random (standard Gaussian) instance of a convex cone program in terms of the intrinsic volumes and curvature measures of the reference cone. We then compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions in terms of integrals related to Mehta’s integral. In particular, we obtain a closed formula for the probability that the solution of a random (standard Gaussian) semidefinite program has a certain rank.