正弦余弦算法求解线性互补问题的最小范数解  

Minimum norm solution to linear complementarity problem by sine cosine algorithm

作　　者：雍龙泉[1] 贾伟 黎延海[1] YONG Longquan;JIA Wei;LI Yanhai(School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001

出　　处：《安徽大学学报（自然科学版）》2022年第1期1-6,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(1401357);陕西省教育厅重点科学研究计划项目(20JS021);陕西省教育厅专项科研计划项目(17JK0146);陕西理工大学科研项目(SLGYQZX2002)。

摘　　要：针对存在多个解的线性互补问题,找出尽可能多的解,进而在众多解中寻找最小范数解,成为当前的一个研究热点.论文通过把线性互补问题转化为绝对值方程,定义了智能算法的适应值函数,采用正弦余弦算法求解线性互补问题,在其中选取范数最小的解.数值结果表明该方法能够找到原问题尽可能多的最小范数解,可为研究其稀疏解提供一些近似结果.For the linear complementarity problem(LCP)with multiple solutions,finding as many solutions as possible and then selecting the minimum norm solution among the solutions had become a research hotspot.By transforming the linear complementarity problem into the absolute value equation(AVE),the fitness function of the intelligent algorithm was defined,and the sine and cosine algorithm(SCA)was applied to solve LCP,and then the minimum norm solution to LCP was selected.Numerical results shown that the method can find the minimum norm solution to the original problem as many as possible,and that provided some approximate results for the sparse solution to LCP in some sense.

关 键 词：多个解的线性互补问题 最小范数解 绝对值方程 适应值函数 正弦余弦算法 

分 类 号：O221[理学—运筹学与控制论] O241[理学—数学]