I am new to optimization stuff. I need to formulate and solve this optimization problem.
$$\min \sum_{t\in\mathcal{T}}p_t$$
s.t. $$\sum_{t\in \mathcal{T}}w_t\log_2\left(1+\frac{h}{w_tn_0}p_t\right)= D$$
or
$$\sum_{t\in \mathcal{T}}w_t\ln\left(1+\frac{h}{w_tn_0}p_t\right)= S$$
Here, $p_t$ is the optimization variable.
Here, $h$, $w_t$, $n_0$ and $D$/$S$ are real and positive and great than $0$, and they are known. $\mathcal{T}$ is index set with $T$ elements, i.e., $\mathcal{T}=\{1,2,\cdots, T\}$.
Somone please help me to solve this.How can I express $p_t$.
