Does kkt condition do the partial differential to the lagrange multiplier i wanted,and set the equation become zero? i mean,
$L=P_E+\alpha [P_T-\sum\limits _{k=1}^{K}p_k]+\gamma [\sum\limits _{j=1}^{K}p_j|h_kf_k|^2 + \sigma^2_{a_{k}}-\frac{P}{1-\rho_k}]+\mu[\frac{p_k |h_kf_k|^2}{\bar \gamma}-\sum\limits_{k \neq j}p_j|h_kf_k|^2- \sigma^2_{a_{k}}-\frac{\sigma^2_{d_{k}}}{1-\rho_k}]$
$\alpha,\mu $ and $\gamma$ are lagrange multiplier,so if i do the kkt condition ,it means that i do partial differential to $\alpha,\mu $ and $\gamma$ and set the formula to be zero,that is
$[P_T-\sum\limits _{k=1}^{K}p_k]=0$ , $[\sum\limits _{j=1}^{K}p_j|h_kf_k|^2 + \sigma^2_{a_{k}}-\frac{P}{1-\rho_k}]=0$ and $[\frac{p_k |h_kf_k|^2}{\bar \gamma}-\sum\limits_{k \neq j}p_j|h_kf_k|^2- \sigma^2_{a_{k}}-\frac{\sigma^2_{d_{k}}}{1-\rho_k}]=0$,so if and just set some parameter are known,and use matlab to do calculate the equation ,and i can get the solution i want,take $\rho$ for example.
Is KKT condition actually like this?