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1. 发明授权

US08812278B2 Sobolev Pre-conditioner for optimizing III-conditioned functionals 有权
标题翻译： Sobolev预调节器，用于优化III条件功能
公开(公告)号：US08812278B2
公开(公告)日：2014-08-19
申请号：US13434216
申请日：2012-03-29
申请人： Pushkar P. Joshi , Nathan A. Carr , Tobias O. Martin
发明人： Pushkar P. Joshi , Nathan A. Carr , Tobias O. Martin
IPC分类号： G06F17/50 , G06F17/11
CPC分类号： G06F17/11 , G06F17/50
摘要： Methods and apparatus for providing Sobolev pre-conditioning for optimizing ill-conditioned functionals. A power n is initialized to a maximum power (e.g., 8). For k (e.g., 10) iterations of an optimization pipeline, a matrix M is built by considering all powers of the Laplacian matrix up to the power indicated by n, the Sobolev gradient is computed from the standard gradient, and the computed Sobolev gradient is passed to a numerical optimizer. After the k iterations are complete, if n is at a minimum power (e.g., 1), then the algorithm resets n to the maximum power. Otherwise, n is decremented. For the next k iterations, the matrix M is again built by considering all powers of the Laplacian matrix up to the power indicated by the current value of n. This method is continued until all iterations have completed or until some other terminating condition is reached.
摘要翻译：提供Sobolev预处理以优化病态功能的方法和设备。功率n被初始化为最大功率（例如8）。对于优化流水线的k（例如10）迭代，通过考虑拉普拉斯矩阵的所有功率直到n指示的功率来构建矩阵M，从标准梯度计算Sobolev梯度，并且计算的Sobolev梯度为传递给数值优化器。在k次迭代完成之后，如果n处于最小功率（例如，1），则算法将n重置为最大功率。否则，n递减。对于下一个k次迭代，矩阵M再次通过考虑拉普拉斯矩阵的所有功率直到由当前值n指示的功率来构建。继续这种方法，直到所有的迭代都已经完成或者直到达到一些其它终止条件为止。

2. 发明申请

US20130124160A1 Sobolev Pre-conditioner for Optimizing Ill-Conditioned Functionals 有权
标题翻译：用于优化病态功能的Sobolev预调节器
公开(公告)号：US20130124160A1
公开(公告)日：2013-05-16
申请号：US13434216
申请日：2012-03-29
申请人： Pushkar P. Joshi , Nathan A. Carr , Tobias O. Martin
发明人： Pushkar P. Joshi , Nathan A. Carr , Tobias O. Martin
IPC分类号： G06F17/10
CPC分类号： G06F17/11 , G06F17/50
摘要： Methods and apparatus for providing Sobolev pre-conditioning for optimizing ill-conditioned functionals. A power n is initialized to a maximum power (e.g., 8). For k (e.g., 10) iterations of an optimization pipeline, a matrix M is built by considering all powers of the Laplacian matrix up to the power indicated by n, the Sobolev gradient is computed from the standard gradient, and the computed Sobolev gradient is passed to a numerical optimizer. After the k iterations are complete, if n is at a minimum power (e.g., 1), then the algorithm resets n to the maximum power. Otherwise, n is decremented. For the next k iterations, the matrix M is again built by considering all powers of the Laplacian matrix up to the power indicated by the current value of n. This method is continued until all iterations have completed or until some other terminating condition is reached.
摘要翻译：提供Sobolev预处理以优化病态功能的方法和设备。功率n被初始化为最大功率（例如8）。对于优化流水线的k（例如10）迭代，通过考虑拉普拉斯矩阵的所有功率直到n指示的功率来构建矩阵M，从标准梯度计算Sobolev梯度，并且计算的Sobolev梯度为传递给数值优化器。在k次迭代完成之后，如果n处于最小功率（例如，1），则算法将n重置为最大功率。否则，n递减。对于下一个k次迭代，矩阵M再次通过考虑拉普拉斯矩阵的所有功率直到由当前值n指示的功率来构建。继续这种方法，直到所有的迭代都已经完成或者直到达到一些其它终止条件为止。

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