【摘要】 广义绝对值方程是绝对值方程的推广,证明了其等价于广义线性互补问题,探讨了广义绝对值方程解唯一存在的条件,这些结果也推广了Mangasarian在文献[1]中的结论,提出了广义绝对值方程解唯一存在的几个充要条件.最后,给出了广义绝对值方程的一个迭代算法,理论分析和数值结果均说明该方法是有效的.更多还原

【Abstract】 This paper is concerned with the generalized absolute value equations. It shows that the generalizeda bsolute value equations are equivalent to the generalized linear complementarity problem and a bilinear program. Existence results of the generalized absolute value equations solution are obtained and the results of Mangasarian in [2] are improved. Some necessary and sufficient conditions are given. An iterative algorithm is proposed for the generalized absolute value equations. Theoretic analysis and numerical results show that the method is effective.更多还原