Distance majorization and its applications.
Distance majorization and its applications.
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DOI：
10.1007/s10107-013-0697-1
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发表时间：
2014-08-01
影响因子：
2.7
通讯作者：
Lange, Kenneth
中科院分区：
文献类型：
--
作者：
Chi, Eric C.;Zhou, Hua;Lange, Kenneth
关键词：
闭凸集交上连续可微凸函数极小化问题是应用数学中普遍存在的问题。当它很容易投射到每一个单独的集合上，但投射到它们的交集上时，它特别有趣。基于牛顿法的算法，如内点法，适用于小到中等规模的问题。然而，统计学、工程学和机器学习的现代应用可能会带来数万个或更多参数的问题。我们重新审视这个凸规划问题，并提出了一个算法，规模以及与维度。我们的建议是一个连续的无约束最小化技术的一个实例，并围绕三个想法：优化最小化原则，经典的惩罚方法约束优化，拟牛顿加速定点算法。我们的距离优化算法的性能说明在几个应用程序。
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton’s method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.
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影响因子：
2.1
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