I have a problem minimizing sum of piecewise linear functions. Given $f:R\rightarrow R$ with $f(x) = \sum_{i=1}^n \max (a_ix,b_ix+c_i)$ and $a_i,c_i <0; b_i>0$ find an equation that $a_i,b_i, c_i $ must satisfy in order to assure that argmin of $f$ is $x_0$.
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