Absolute value equations
Absolute value equations
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DOI：
10.1016/j.laa.2006.05.004
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发表时间：
2006-12-01
影响因子：
1.1
通讯作者：
Meyer, R. R.
中科院分区：
文献类型：
--
作者：
Mangasarian, O. L.;Meyer, R. R.
本文研究了含有变量绝对值的NP-难方程：Ax - vertical bar x vertical bar = B，其中A是任意n × n的真实的矩阵.利用与线性互补问题的等价关系，给出了这类绝对值方程解的存在性结果，并在特殊情况下给出了求解方法。我们也给出了不存在的结果，我们的AVE使用定理的替代和其他参数。(c)2006年爱思唯尔公司All rights reserved.
We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax - vertical bar x vertical bar = b, where A is an arbitrary n x n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments. (c) 2006 Elsevier Inc. All rights reserved.