A practical but rigorous approach to sum-of-ratios optimization in geometric applications
A practical but rigorous approach to sum-of-ratios optimization in geometric applications
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DOI：
10.1007/s10589-012-9488-5
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发表时间：
2012-05
影响因子：
2.2
通讯作者：
Takahito Kuno;Toshiyuki Masaki
中科院分区：
文献类型：
--
作者：
Takahito Kuno;Toshiyuki Masaki
本文给出了一个极小化向量的Lq范数的算法，其中q是一个任意正整数，其分量是线性分式函数。该问题是一种比率和优化问题，在计算机视觉中经常出现。在这种情况下，它的特点是大量的比率和少量的变量。我们在这里提出的算法利用这一功能，并产生一个全局最优的解决方案，在一个实际的计算时间。
In this paper, we develop an algorithm for minimizing theLqnorm of a vector whose components are linear fractional functions, whereqis an arbitrary positive integer. The problem is a kind of sum-of-ratios optimization problem, and often occurs in computer vision. In that case, it is characterized by a large number of ratios and a small number of variables. The algorithm we propose here exploits this feature and generates a globally optimal solution in a practical amount of computational time.