The problem of optimal smoothing for convex functions
The problem of optimal smoothing for convex functions
复制标题
凸函数的最优平滑问题
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Ghomi
中科院分区：
文献类型：
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作者：
M. Ghomi
本文描述了一个光滑凸函数的过程，它不仅保持凸性，而且在适当的条件下，在几乎所有已经光滑的区域上保持函数不变。该方法基于卷积，然后是胶合。控制的Hessian函数的结果是这个过程的关键，它表明，它可以成功地完成提供的原始函数是严格凸的光滑区域的边界。
A procedure is described for smoothing a convex function which not only preserves its convexity, but also, under suitable conditions, leaves the function unchanged over nearly all the regions where it is already smooth. The method is based on a convolution followed by a gluing. Controlling the Hessian of the resulting function is the key to this process, and it is shown that it can be done successfully provided that the original function is strictly convex over the boundary of the smooth regions.