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 旋转锥面$l_\infty$拟合的截断光滑化牛顿法 引用本文： 肖瑜,于波,王德伦.旋转锥面$l_\infty$拟合的截断光滑化牛顿法[J].数学研究与评论,2010,30(1):159-166. 作者姓名： 肖瑜  于波  王德伦 作者单位： 大连理工大学数学科学学院, 辽宁 大连 116024;大连理工大学数学科学学院, 辽宁 大连 116024;大连理工大学机械工程学院, 辽宁 大连 116024 基金项目： 国家自然科学基金(Grant No.10671029);博士点基金(Grant No.20060141029). 摘    要： In this paper, the rotated cone fitting problem is considered. In case the measured data are generally accurate and it is needed to fit the surface within expected error bound, it is more appropriate to use l∞ norm than 12 norm. l∞ fitting rotated cones need to minimize, under some bound constraints, the maximum function of some nonsmooth functions involving both absolute value and square root functions. Although this is a low dimensional problem, in some practical application, it is needed to fitting large amount of cones repeatedly, moreover, when large amount of measured data are to be fitted to one rotated cone, the number of components in the maximum function is large. So it is necessary to develop efficient solution methods. To solve such optimization problems efficiently, a truncated smoothing Newton method is presented. At first, combining aggregate smoothing technique to the maximum function as well as the absolute value function and a smoothing function to the square root function, a monotonic and uniform smooth approximation to the objective function is constructed. Using the smooth approximation, a smoothing Newton method can be used to solve the problem. Then, to reduce the computation cost, a truncated aggregate smoothing technique is applied to give the truncated smoothing Newton method, such that only a small subset of component functions are aggregated in each iteration point and hence the computation cost is considerably reduced. 关 键 词： 光滑牛顿法  转锥  截断  拟合  平滑技术  绝对值函数  函数功能  牛顿方法 收稿时间： 2009/7/26 0:00:00 修稿时间： 2009/11/2 0:00:00 Truncated Smoothing Newton Method for $l_\infty$ Fitting Rotated Cones Yu XIAO,Bo YU and De Lun WANG.Truncated Smoothing Newton Method for $l_\infty$ Fitting Rotated Cones[J].Journal of Mathematical Research and Exposition,2010,30(1):159-166. Authors: Yu XIAO  Bo YU and De Lun WANG Institution: School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China;School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China;School of Mechanical Engineering, Dalian University of Technology, Liaoning 116024, P. R. China Abstract: In this paper, the rotated cone fitting problem is considered. In case the measured data are generally accurate and it is needed to fit the surface within expected error bound, it is more appropriate to use $l_\infty$ norm than $l_2$ norm. $l_\infty$ fitting rotated cones need to minimize, under some bound constraints, the maximum function of some nonsmooth functions involving both absolute value and square root functions. Although this is a low dimensional problem, in some practical application, it is needed to fitting large amount of cones repeatedly, moreover, when large amount of measured data are to be fitted to one rotated cone, the number of components in the maximum function is large. So it is necessary to develop efficient solution methods. To solve such optimization problems efficiently, a truncated smoothing Newton method is presented. At first, combining aggregate smoothing technique to the maximum function as well as the absolute value function and a smoothing function to the square root function, a monotonic and uniform smooth approximation to the objective function is constructed. Using the smooth approximation, a smoothing Newton method can be used to solve the problem. Then, to reduce the computation cost, a truncated aggregate smoothing technique is applied to give the truncated smoothing Newton method, such that only a small subset of component functions are aggregated in each iteration point and hence the computation cost is considerably reduced. Keywords: rotated cone fitting  nonsmooth optimization  minimax problem  $l_\infty$ fitting  smoothing Newton method 本文献已被 维普 等数据库收录！ 点击此处可从《数学研究与评论》浏览原始摘要信息 点击此处可从《数学研究与评论》下载免费的PDF全文