基于调节熵函数的光滑牛顿法求解绝对值方程

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英文篇名：A smooth Newton method to absolute value equation based on adjustable entropy function 作者：雍龙泉 英文作者：Yong Long-quan;School of Mathematics and Computer Science,Shaanxi University of Technology; 关键词：绝对值方程 ; 绝对值函数 ; 一致光滑逼近函数 ; 调节熵函数 ; 光滑牛顿法 英文关键词：absolute value equation;;absolute value function;;uniform smooth approximation function;;adjustable entropy function;;smooth Newton method 中文刊名：LDZK 英文刊名：Journal of Lanzhou University(Natural Sciences) 机构：陕西理工大学数学与计算机科学学院; 出版日期：2016-08-15 出版单位：兰州大学学报(自然科学版) 年：2016 期：v.52;No.226 基金：国家自然科学基金项目(11401357);; 陕西省青年科技新星项目(2016KJXX-95);; 陕西省教育厅科研项目(16JK1150);; 陕西理工大学科研计划项目(SLGKYQD2-14) 语种：中文; 页：LDZK201604020 页数：6 CN：04 ISSN：62-1075/N 分类号：116-120+127

摘要

绝对值方程Ax-|x|=b等价于一个不可微的NP-hard优化问题.构造了绝对值函数的一致光滑逼近函数,采用一致光滑逼近函数对绝对值方程光滑化处理,引入适当的目标函数,给出了求解绝对值方程的光滑牛顿法.数值实验结果证明了该方法的有效性.
        An absolute value equation is equivalent to a non-differentiable NP-hard optimization problem in its general form.This paper transformed the absolute value equation into a differentiable optimization by establishing a uniform smooth approximation function of absolute value function,and a smooth Newton method was proposed for solving absolute value equation by introducing a proper targeted function.Numerical results indicated that the method is effective.

引文

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