夹心熵与相关优化问题的强凸性
泛函分析
2018-10-17 v2
摘要
我们给出关于夹心准相对熵（经典保真度的一个参数化版本）的严格凸性与强凸性，以及高阶微分公式的若干定理。这些结论对于确立针对这些函数的优化问题的梯度投影算法的全局线性收敛性至关重要。经典保真度的情形对于高斯测度的多边际最优传输问题（即 -耦合问题）具有特殊意义。
引用
@article{arxiv.1807.00978,
title = {Strong Convexity of Sandwiched Entropies and Related Optimization Problems},
author = {Rajendra Bhatia and Tanvi Jain and Yongdo Lim},
journal= {arXiv preprint arXiv:1807.00978},
year = {2018}
}
备注
In one of the statements of Theorem 4 of the first version of this paper, an extra condition that is needed was missing. This has been corrected in the present version, where that Theorem is now Theorem 5. The rest of the paper is unaffected