# Non linear optimization

this is a convex problem with non-linear constraint as well as nonlinear objective function \rho\geq \rho_{min} ,i have tried many times it in fmincon matlab under various headings but i am not getting results. Now, i have to go into cvx. I will be obliged if anyone could help me to solve it. Thanks a ton in advance. Please give me a routine to solve it.plzzzzzzzz
\begin{equation}
\underset{p_{s},p_{r}} {\text {minimize}}
\quad C = w_1.(\frac{p_{s}+p_{r}}{p_{max}}) + w_2.{\frac{\rho_{min}}{\rho}}
\end{equation}
\begin{equation}
\begin{aligned}
\text{subject to}
& \rho\geq \rho_{min},\quad \text{non linear constraint} \newline
& p_{s}\geq 0, p_{r}\geq 0.
\end{aligned}
\end{equation}

where , \begin{equation}
\begin{aligned}
& \rho = \frac{\phi_{1}\phi_{2}p_{s}p_{r}}{\phi_{1}p_{s} + \phi_{2}p_{r} + 1}\newline &w_{1}+w_{2}=1,& w_{1}=.5,w_{2}=.5 \newline &\phi_{1}=6.7;
\phi_{2}=7.5 \quad(\text{i have to repeat it for 10000 different values of \phi_1 \& \phi_2)} \newline