| 绝对值方程研究进展 |
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| 引用本文： | 雍龙泉,张社民,张建科,王会战.绝对值方程研究进展[J].陕西工学院学报,2012(1):33-38. |
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| 作者姓名： | 雍龙泉 张社民 张建科 王会战 |
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| 作者单位： | [1]陕西理工学院数学与计算机科学学院,陕西汉中723001 [2]西安邮电学院理学院,陕西西安710121 |
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| 基金项目： | 陕西省教育厅科研计划项目（11JK1051）; 陕西理工学院博士科研启动基金资助项目（SLGQD0801） |
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| 摘 要： | 线性规划、二次规划、双矩阵对策等问题都能转化为线性互补问题,而线性互补问题又可以归结为绝对值方程,因此研究绝对值方程具有重要的意义。绝对值方程是一个NP-hard问题,对绝对值方程的研究现状进行了分析,给出了绝对值方程的理论研究现状,总结了绝对值方程的若干求解算法。这些算法可以归结为三类：1）逐次线性化方法,2）半光滑牛顿法,3）光滑牛顿法。指出解的存在性、构造光滑函数、采用智能算法求解以及算法收敛性分析将成为绝对值方程的研究热点。
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| 关 键 词： | 绝对值方程 线性互补问题 牛顿法 光滑函数法 |
Advance in the study of absolute value equations |
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| YONG Long-quan,ZHANG She-min,ZHANG Jian-ke,WANG Hui-zhan.Advance in the study of absolute value equations[J].Journal of Shaanxi Institute of Technology,2012(1):33-38. |
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| Authors: | YONG Long-quan ZHANG She-min ZHANG Jian-ke WANG Hui-zhan |
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| Affiliation: | 1. School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723001, China; 2. School of Science, Xi＇an University of Posts and Telecommunications, Xi＇an 710121, China) |
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| Abstract: | The significance of the absolute value equations （AVE） arises from the fact that linear programs, quadratic programs, bimatrix games and other problems can all be reduced to the linear com- plementarity problem that in turn is equivalent to the AVE. AVE is an NP-hard problem in its general form. The current research situation of AVE was analyzed. Results of AVE in theory were given, and the algorithms for AVE can be summarized into three categories： 1 ） successive linearization method; 2） semi-smooth Newton method; 3 ） Smoothing Newton method. Combining with the author studies, it is concluded that ＂existence of solution, constructing smoothing function, using intelligent algorithms and convergence analysis＂ will be the research focuses on AVE. |
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| Keywords: | absolute value equations linear complementarity problem Newton method smoothing function method |
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