谱投影梯度算法求解绝对值方程最小1范数解  

Spectral projection gradient method for minimum 1-norm solution to absolute value equation

作　　者：王爱祥 WANG Ai-xiang(School of Mathematics,China University of Mining and Technology,Xuzhou 221008,China;School of Aerospace and Mechanical Engineering,Changzhou Institute of Technology,Changzhou 213032,China)

机构地区：[1]中国矿业大学数学学院,江苏徐州221008 [2]常州工学院航空与机械工程学院,江苏常州213032

出　　处：《陕西理工大学学报（自然科学版）》2023年第1期80-85,共6页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(72071202)。

摘　　要：为研究绝对值方程最小1范数解的求解问题,通过绝对值运算的等价代换,把绝对值方程求解问题转化为光滑函数的优化问题;再利用罚函数的思想,建立了非负约束的二次规划问题,进而使用谱投影梯度算法求解;最后进行了数值实验。理论分析和数值结果都表明了算法的有效性;该方法回避了直接求解非光滑的绝对值方程,且使转化后的优化问题具有非负约束,便于求解;该算法具有全局收敛性,对目前提出的智能算法缺乏理论上的收敛性问题是一个算法上的补充。The problem of solving the minimum 1-norm solution of the absolute value equation is mainly studied in this paper. Based on equivalent substitution of absolute value operation, the problem of solving the absolute value equation is firstly transformed into the optimization problem of smooth function. Secondly, the quadratic programming problem with non negative constraints is established by using the idea of penalty function. Thirdly, spectral projection gradient algorithm is used to solve the problem. Finally, numerical experiments are carried out. Theoretical analysis and numerical results show the effectiveness of the algorithm. This method avoids directly solving the nonsmooth absolute value equation, and makes the feasible region of the problem nonnegative, which is easy to solve. The algorithm has global convergence, which is a supplement to the current intelligent algorithm.

关 键 词：绝对值方程 最小1范数解 谱投影梯度法 

分 类 号：O242.2[理学—计算数学]