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
georgefarnandez Paul Rubin ♦♦ |

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
Paul Rubin ♦♦ |