符号控制的绝对值方程求解器及其在支持向量机中的应用
Sign controlled solvers for the absolute value equation with an application to support vector machines
摘要：
设$A$是一个实$n\times n$矩阵，而$z,b\in \mathbb R^n$ .分段线性方程组$z-A\vert z\vert = b$称为绝对值方程。它等价于一般的线性互补性问题，因而一般是NP难的.关于后者的问题，三个解决方案：一个直接的，一个半迭代和一个离散变量的阻尼牛顿。他们以前证明的范围内的正确性和收敛性，分别延长。它们的性能进行比较的XOR分离问题的支持向量机，可以重新制定为一个绝对值方程的实例。
英文摘要：
Let $A$ be a real $n\times n$ matrix and $z,b\in \mathbb R^n$. The piecewise linear equation system $z-A\vert z\vert = b$ is called an absolute value equation. It is equivalent to the general linear complementarity problem, and thus NP hard in general. Concerning the latter problem, three solvers are presented: One direct, one semi-iterative and one discrete variant of damped Newton. Their previously proved ranges of correctness and convergence, respectively, are extended. Their performance is compared on instances of the XOR separation problem for support vector machines which can be reformulated as an absolute value equation.
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