关于非线性L_1回归的算法

^ON SOME COMPUTATION METHODS OF THE NONLINEAR L_1-NORM ESTIMATION IN REGRESSION

关于非线性Ｌ_１回归的算法杨自强（中国科学院计算中心）ＯＮＳＯＭＥＣＯＭＰＵＴＡＴＩＯＮＭＥＴＨＯＤＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＬ_１－ＮＯＲＭＥＳＴＩＭＡＴＩＯＮＩＮＲＥＧＲＥＳＳＩＯＮ￥ＹａｎｇＺｉ－ｑｉａｎｇ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ．Ａ...

Abstract In this paper, Some computation methods of the nonlinear L1-norm estimation in regression are introduced and reviewed. They contain three kinds of algorithms as follows. i) Reducing a nonlinear L1-norm problem to sequential linear L1-norm problems. ii) Iteratively reweighted method of least squares. iii) Algorithms based on smooth approx imation presented by EI-Attar et al. (1979), Fishier-Zang (1982)and the present author, Yang (1990). Especially, Yang's algorithm is introduced in some detail. We Point out that both Fishier-Zang's algorithm and the iteratively reweighted method of least squares are the special cases of Yang's.