An Active Set-Type Newton Method for Constrained Nonlinear Systems
An Active Set-Type Newton Method for Constrained Nonlinear Systems
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DOI：
10.1007/978-1-4757-3279-5_9
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发表时间：
2001
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影响因子：
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通讯作者：
Christian Kanzow
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文献类型：
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作者：
Christian Kanzow
我们考虑的问题，找到一个解决方案的非线性方程组的一些框约束。为此，我们引入了一个新的活动集型牛顿法。该方法是全局收敛的，在这个意义上，每个聚点是一个相应的框约束优化问题的稳定点。在适当的正则性条件下，该方法是局部超线性或二次收敛的。此外，该方法产生可行的迭代，并在每次迭代中只需求解一个线性方程组。由于我们的活动集策略，这个线性系统的维度降低了。一些初步的数值结果。
We consider the problem of finding a solution of a nonlinear system of equations subject to some box constraints. To this end, we introduce a new active set-type Newton method. This method is shown to be globally convergent in the sense that every accumulation point is a stationary point of a corresponding box constrained optimization problem. Moreover, the method is locally superlinearly or quadratically convergent under a suitable regularity condition. Furthermore the method generates feasible iterates and has to solve only one linear system of equations at each iteration. Due to our active set strategy, this linear system is of reduced dimension. Some preliminary numerical results are included.