r_{d,k} 和 \eta_{mk} 是我的优化变量
You haven’t even told us what the optimization variables are, as opposed to input data.
\begin{aligned}
&\operatorname*{min}_{\boldsymbol{f},\boldsymbol{r_{d}},\boldsymbol{r_{u}},\boldsymbol{\nu},\boldsymbol{\mu},\boldsymbol{\tilde{v}},t_{d},t_{c},t_{u}} (t_d+t_c+t_u)\\
&\text{s.t.} f_{min}\leq f_{k} \leq f_{max} &(1)\\
&0\leq r_{d,k},0\leq r_{u,k}\quad\forall k &(2)\\
&\frac{a_{k}S_{d}}{r_{d,k}}\leq t_{d}\quad\forall k,a_{k}\neq0 &(3)\\
&\frac{a_{k}S_{u}}{r_{u,k}}\leq t_{u}\quad\forall k,a_{k}\neq0&(4)\\
&\frac{a_{k}LD_{k}c_{k}}{f_{k}}\leq t_{c}\quad\forall k,a_{k}\neq0 &(5)\\
&\tilde{v}_{mk}\leq a_{k}\quad\forall m,k &(6)\\
&\sum_{k \in\mathcal{K}} \tilde{v}_{mk}\leq 1\quad\forall m &(7)\\
&\sigma_{mk}^{2}\nu_{mk}^{2}\leq\tilde{v}_{mk}\quad\forall m,k &(8)\\
&0\leq\nu_{mk}\quad\forall m,k &(9)\\
&u_{k}^{2}\leq a_{k}\quad\forall m,k &(10)\\
&0\leq \mu_{k}\leq1\quad\forall k &(11)\\
&0\leq r_{d,k}\leq R_{d,k}(\mathbf{\boldsymbol{\nu}})\quad\forall k &(12) \\
&0\leq r_{u,k}\leq R_{u,k}(\boldsymbol{\mu})\quad\forall k &(13)
\end{aligned}
The specific expressions for R_{d,k}(\boldsymbol{\nu}) and R_{u,k}(\boldsymbol{\mu}) are as follows:
R_{d,k}(\boldsymbol{\nu})=\frac{\tau_{c}-\tau_{t}}{\tau_{c}}B\log_{2}\left(1+\frac{\rho_{d}\left(\sum_{m\in\mathcal{M}}\nu_{mk}{\sigma}_{mk}^{2}\right)^{2}}{\underbrace{\rho_{d}\sum_{\ell\in\mathcal{K}\setminus k}\left(\sum_{m\in\mathcal{M}}\nu_{m\ell}{\sigma}_{m\ell}^{2}\frac{\beta_{mk}}{\beta_{m\ell}}\right)^{2}|\boldsymbol{\varphi}_{\ell}^{H}\boldsymbol{\varphi}_{k}|^{2}}_{\text{Pilot comanination}}+\underbrace{\rho_{d}\sum_{\ell\in\mathcal{K}}\sum_{m\in\mathcal{M}}\nu_{m\ell}^{2}{\sigma}_{m\ell}^{2}{\beta}_{mk}}_{\text{Incer-user interfecence}}+1}\right)
R_{u,k}(\boldsymbol{\mu})=\frac{\tau_{c}-\tau_{t}}{\tau_{c}}B\log_{2}\left(1+\frac{\rho_{u}\mu_{k}^{2}\left(\sum_{{m\in\mathcal{M}}}{\sigma}_{mk}^{2}\right)^{2}}{\underbrace{{\rho_{u}\sum_{\ell\in\mathcal{K}\setminus k}\mu_{\ell}^{2}\left(\sum_{{m\in\mathcal{M}}}{\sigma}_{mk}^{2}\frac{\beta_{m\ell}}{\beta_{mk}}\right)^{2}|\boldsymbol{\varphi}_{k}^{H}\boldsymbol{\varphi}_{\ell}|^{2}}}_{{\text{Phor contamination}}}+\underbrace{\rho_{u}\sum_{\ell\in\mathcal{K}}\mu_{\ell}^{2}\sum_{{m\in\mathcal{M}}}{\sigma}_{mk}^{2}\beta_{m\ell}}_{{\text{Inter-user interforecosce}}}+\sum_{{m\in\mathcal{M}}}{\sigma}_{mk}^{2}}\right)
It looks like this has lost of bilinear terms consisting of products of various subscripts of \nu inside log2. if there is a good convex approximation to this constraint, I certainly don’t know what it would be. I don’t think CVX is an appropriate tool for this problem.
Okay, I understand. Thank you for your answer