Optimality Conditions of a Class of Special Nonsmooth Programming

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.