# How to express this optimization variable as a function of other parameters?

 0 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 $$p_t$$ as a function of others? asked 13 Oct '17, 02:26 georgefarnandez 11●2 accept rate: 0% Paul Rubin ♦♦ 14.6k●5●13

 0 I removed the tag "convex-optimization" from your question, because your model is nonconvex as the result of nonlinear equation constraints. Solving nonconvex problems is generally a pain, but if you only have the one equation constraint, you might look at the Lagrange multiplier method. If you also have bounds on $$p_t$$ (for instance, $$p_t\ge 0$$), you should probably look at the KKT conditions. answered 13 Oct '17, 11:48 Paul Rubin ♦♦ 14.6k●5●13 accept rate: 19%
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