Some Noninterior Continuation Methods for Linear Complementarity Problems
Some Noninterior Continuation Methods for Linear Complementarity Problems
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DOI：
10.1137/s0895479894273134
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发表时间：
1996-10
期刊：
影响因子：
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通讯作者：
C. Kanzow
中科院分区：
文献类型：
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作者：
C. Kanzow
我们介绍了一些新的路径跟踪方法解决线性互补问题。我们称这些方法为非内部连续方法，因为与邻近点方法相比，并非所有迭代都必须保持在正正交中。这是可能的，因为我们重新制定某些扰动互补问题作为一个非线性方程组。然而，类似于邻点方法，我们也试图遵循中心路径，我们提出了一些条件，保证这条中心路径的存在，证明了一些可实现的非内部连续方法的全局收敛性结果，并报告了一些数值结果与这些方法得到的。我们还证明了扰动线性互补问题的全局误差界结果。
We introduce some new path-following methods for the solution of the linear complementarity problem. We call these methods noninterior continuation methods since, in contrast to interior-point methods, not all iterates have to stay in the positive orthant. This is possible since we reformulate certain perturbed complementarity problems as a nonlinear system of equations. However, similar to interior-point methods, we also try to follow the central path. We present some conditions which guarantee the existence of this central path, prove a global convergence result for some implementable noninterior continuation methods, and report some numerical results obtained with these methods. We also prove global error bound results for the perturbed linear complementarity problems.