Volume 21, Issue 6
Optimality Conditions of a Class of Special Nonsmooth Programming
DOI:

J. Comp. Math., 21 (2003), pp. 791-800

Published online: 2003-12

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• Abstract

In this paper, we investigate the optimality conditions of a class of special nonsmooth programming $\min F(x)=\sum_{i=1}^m|\max\{f_i(x),c_i\}|$ which arises from $L_1-$norm optimization, where $c_i\in R$ is constant and $f_i\in C^1,i=1,2,\cdots,m.$ these conditions can easily be tested by computer.

• Keywords

Generalized gradient Directional derivative Optimality conditions Nonsmooth programming

@Article{JCM-21-791, author = {Song-bai Sheng and Hui-fu Xu }, title = {Optimality Conditions of a Class of Special Nonsmooth Programming}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {6}, pages = {791--800}, abstract = { In this paper, we investigate the optimality conditions of a class of special nonsmooth programming $\min F(x)=\sum_{i=1}^m|\max\{f_i(x),c_i\}|$ which arises from $L_1-$norm optimization, where $c_i\in R$ is constant and $f_i\in C^1,i=1,2,\cdots,m.$ these conditions can easily be tested by computer. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10235.html} }
TY - JOUR T1 - Optimality Conditions of a Class of Special Nonsmooth Programming AU - Song-bai Sheng & Hui-fu Xu JO - Journal of Computational Mathematics VL - 6 SP - 791 EP - 800 PY - 2003 DA - 2003/12 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10235.html KW - Generalized gradient KW - Directional derivative KW - Optimality conditions KW - Nonsmooth programming AB - In this paper, we investigate the optimality conditions of a class of special nonsmooth programming $\min F(x)=\sum_{i=1}^m|\max\{f_i(x),c_i\}|$ which arises from $L_1-$norm optimization, where $c_i\in R$ is constant and $f_i\in C^1,i=1,2,\cdots,m.$ these conditions can easily be tested by computer.