# how to minimize this convex function?

$x_i$ and $y_j$ are variables.

I intend to minimize this function and obtain the optimal value of $x$ and $y$:

\begin{align} \frac{A_1}{y1}+B_1y_1+\frac{O1}{x1}+c_1\max\{x_1,y_1\}+\frac{A_2}{y1}+B_1y_1+\frac{O3}{x3}+c_3\max\{x_3,y_1\}+\frac{A2}{y2}+b_2y_2+C_2\max\{x_1,y_2\} \end{align}

• Presumably you have some constraints (e.g. $x_1,y_1,y_2>0$)? Could you write $(A_1+A_2)/y_1$ instead of both summands? In any case: Use case distinction and derive. – Dirk Oct 6 '13 at 18:57
• yes,all variables are positive.how to distinct? – mobina Oct 7 '13 at 7:33