摘要
研究线性互补问题解的存在性 ,发现一例 ,用 L emke算法找不到解 ,用特殊方法找到一解 .随后提出并证明了线性互补问题解的充分必要条件 .以此为理论基础给出求线性互补问题全部解的算法——整标集法 .此算法具有一般性 ,使用范围广泛 .用它可以求得线性互补问题的全部解 .给出 3个算例 ,用 3种方法求解 .对于其中的每一个 ,用整标集法都找到了许多解 .然而 ,其中两例用 L emke算法均没有找到解 .最后指明了原因 .
When the author studied on the existence of the solution to linear complementary problems,one example was discovered.No solution could be obtained by Lemkes complementary pivoting algorithm,but one solution was obtained by a special method.Consequently the necessary and sufficient conditions of the solution for linear complementary problem (LCP) were introduced,and the algorithm--integer sets method--for finding all solutions to LCP was presented.All complementary feasible solutions to LCP may be found by this algorithm.Three examples are given and three methods were used to finding their solutions.For each of them,there are many solutions obtained by the integer sets method.However,for two of them,no solution was obtained by Lemkes algorithm.Finally,the reason was explained.
出处
《天津大学学报（自然科学与工程技术版）》
EI
CAS
CSCD
北大核心
2001年第5期582-586,共5页
Journal of Tianjin University：Science and Technology
