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

Song-Bai Sheng & Hui-Fu Xu

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 $\min F(x)=\sum\limits_{i=1}^m|\max\{f_i(x),c_i\}|$ 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.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-21-791, author = {Sheng , Song-Bai and Xu , Hui-Fu}, 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 $\min F(x)=\sum\limits_{i=1}^m|\max\{f_i(x),c_i\}|$ 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 - Sheng , Song-Bai AU - Xu , Hui-Fu 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, Directional derivative, Optimality conditions, Nonsmooth programming. AB -

In this paper, we investigate the optimality conditions of a class of special nonsmooth programming $\min F(x)=\sum\limits_{i=1}^m|\max\{f_i(x),c_i\}|$ 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.

Sheng , Song-Bai and Xu , Hui-Fu. (2003). Optimality Conditions of a Class of Special Nonsmooth Programming. Journal of Computational Mathematics. 21 (6). 791-800. doi:
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