Hi,every one, I really need your help in solving the following problem:

\begin{gathered} \mathop {\min }\limits_{\mathbf{w}} \;\operatorname{tr} \left[ {{{\left( {\sum\limits_{n = 1}^N {\phi \left( {{w_n}} \right){{\mathbf{A}}_n}} } \right)}^{ - 1}}} \right] \hfill \\ {\text{s}}{\text{.t}}\;\sum\limits_{n = 1}^N {\phi \left( {{w_n}} \right) = L} \hfill \\ \end{gathered}

where {\mathbf{w}} = {\left[ {{w_1}, \cdots ,{w_N}} \right]^{\text{T}}}, \phi \left( x \right) = \frac{1}{{1 + {e^{ - \rho x}}}},\rho \geq 0 and {{\mathbf{A}}_n} \succeq {\mathbf{0}}. I already notice that functions from the exponential family can not be easily handled by cvx. Nevertheless, you have constructed a successive approximation to support the exponential family of functions. How should I solve my problem with the successive approximation in cvx ? Thank you.