常熟理工学院学报
常熟理工學院學報
상숙리공학원학보
JOURNAL OF CHANGSHU INSTITUTE OF TECHNOLOGY
2011年
8期
27-30
,共4页
广义绝对值方程%广义线性互补问题%迭代算法
廣義絕對值方程%廣義線性互補問題%迭代算法
엄의절대치방정%엄의선성호보문제%질대산법
generalized absolute value equations%generalized linear complementarity problem%iterative algorithm
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．
廣義絕對值方程是絕對值方程的推廣，證明瞭其等價于廣義線性互補問題，探討瞭廣義絕對值方程解唯一存在的條件，這些結果也推廣瞭Mangasarian在文獻[1]中的結論，提齣瞭廣義絕對值方程解唯一存在的幾箇充要條件．最後，給齣瞭廣義絕對值方程的一箇迭代算法，理論分析和數值結果均說明該方法是有效的．
엄의절대치방정시절대치방정적추엄，증명료기등개우엄의선성호보문제，탐토료엄의절대치방정해유일존재적조건，저사결과야추엄료Mangasarian재문헌[1]중적결론，제출료엄의절대치방정해유일존재적궤개충요조건．최후，급출료엄의절대치방정적일개질대산법，이론분석화수치결과균설명해방법시유효적．
This paper is concerned with the generalized absolute value equations. It shows that the generalized absolute 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.
