The operation of KKT condition in lagrange function
$begingroup$
Does kkt condition do the partial differential to the lagrange multiplier i wanted,and set the equation become zero? i mean,
$L=P_E+alpha [P_T-sumlimits _{k=1}^{K}p_k]+gamma [sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]+mu[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]$
$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
$[P_T-sumlimits _{k=1}^{K}p_k]=0$ , $[sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]=0$ and $[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]=0$,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?
optimization convex-optimization lagrange-multiplier karush-kuhn-tucker
asked Jan 8 at 6:05
electronic componentelectronic component
407
$endgroup$
add a comment |
$begingroup$
Does kkt condition do the partial differential to the lagrange multiplier i wanted,and set the equation become zero? i mean,
$L=P_E+alpha [P_T-sumlimits _{k=1}^{K}p_k]+gamma [sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]+mu[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]$
$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
$[P_T-sumlimits _{k=1}^{K}p_k]=0$ , $[sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]=0$ and $[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]=0$,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?
optimization convex-optimization lagrange-multiplier karush-kuhn-tucker
asked Jan 8 at 6:05
electronic componentelectronic component
407
$endgroup$
$begingroup$
only if the original constraints were equality constraints to begin with
$endgroup$
– LinAlg
Jan 8 at 17:53
$begingroup$
yes!the formula to be zero is actually the original constraints were equality constraints,so is my thinking right?
$endgroup$
– electronic component
Jan 9 at 0:58
$begingroup$
why don't you have an objective function in your Lagrangian?
$endgroup$
– LinAlg
Jan 9 at 1:40
$begingroup$
@LinAlg i have added it
$endgroup$
– electronic component
Jan 9 at 4:28
$begingroup$
The KKT conditions also include a stationarity condition (which is the derivative of L with respect to the original optimization variable) and a complementary slackness condition.
$endgroup$
– LinAlg
Jan 9 at 13:40
add a comment |
$begingroup$
Does kkt condition do the partial differential to the lagrange multiplier i wanted,and set the equation become zero? i mean,
$L=P_E+alpha [P_T-sumlimits _{k=1}^{K}p_k]+gamma [sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]+mu[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]$
$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
$[P_T-sumlimits _{k=1}^{K}p_k]=0$ , $[sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]=0$ and $[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]=0$,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?
optimization convex-optimization lagrange-multiplier karush-kuhn-tucker
asked Jan 8 at 6:05
electronic componentelectronic component
407
$endgroup$
Does kkt condition do the partial differential to the lagrange multiplier i wanted,and set the equation become zero? i mean,
$L=P_E+alpha [P_T-sumlimits _{k=1}^{K}p_k]+gamma [sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]+mu[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]$
$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
$[P_T-sumlimits _{k=1}^{K}p_k]=0$ , $[sumlimits _{j=1}^{K}p_j|h_kf_k|^2 + sigma^2_{a_{k}}-frac{P}{1-rho_k}]=0$ and $[frac{p_k |h_kf_k|^2}{bar gamma}-sumlimits_{k neq j}p_j|h_kf_k|^2- sigma^2_{a_{k}}-frac{sigma^2_{d_{k}}}{1-rho_k}]=0$,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?
optimization convex-optimization lagrange-multiplier karush-kuhn-tucker
optimization convex-optimization lagrange-multiplier karush-kuhn-tucker
asked Jan 8 at 6:05
electronic componentelectronic component
407
asked Jan 8 at 6:05
electronic componentelectronic component
407
edited Jan 9 at 4:28
electronic component
asked Jan 8 at 6:05
electronic componentelectronic component
407
asked Jan 8 at 6:05
electronic componentelectronic component
407
asked Jan 8 at 6:05
electronic componentelectronic component
407
407
$begingroup$
only if the original constraints were equality constraints to begin with
$endgroup$
– LinAlg
Jan 8 at 17:53
$begingroup$
yes!the formula to be zero is actually the original constraints were equality constraints,so is my thinking right?
$endgroup$
– electronic component
Jan 9 at 0:58
$begingroup$
why don't you have an objective function in your Lagrangian?
$endgroup$
– LinAlg
Jan 9 at 1:40
$begingroup$
@LinAlg i have added it
$endgroup$
– electronic component
Jan 9 at 4:28
$begingroup$
The KKT conditions also include a stationarity condition (which is the derivative of L with respect to the original optimization variable) and a complementary slackness condition.
$endgroup$
– LinAlg
Jan 9 at 13:40
add a comment |
$begingroup$
only if the original constraints were equality constraints to begin with
$endgroup$
– LinAlg
Jan 8 at 17:53
$begingroup$
yes!the formula to be zero is actually the original constraints were equality constraints,so is my thinking right?
$endgroup$
– electronic component
Jan 9 at 0:58
$begingroup$
why don't you have an objective function in your Lagrangian?
$endgroup$
– LinAlg
Jan 9 at 1:40
$begingroup$
@LinAlg i have added it
$endgroup$
– electronic component
Jan 9 at 4:28
$begingroup$
The KKT conditions also include a stationarity condition (which is the derivative of L with respect to the original optimization variable) and a complementary slackness condition.
$endgroup$
– LinAlg
Jan 9 at 13:40
$begingroup$
only if the original constraints were equality constraints to begin with
$endgroup$
– LinAlg
Jan 8 at 17:53
$begingroup$
only if the original constraints were equality constraints to begin with
$endgroup$
– LinAlg
Jan 8 at 17:53
$begingroup$
yes!the formula to be zero is actually the original constraints were equality constraints,so is my thinking right?
$endgroup$
– electronic component
Jan 9 at 0:58
$begingroup$
yes!the formula to be zero is actually the original constraints were equality constraints,so is my thinking right?
$endgroup$
– electronic component
Jan 9 at 0:58
$begingroup$
why don't you have an objective function in your Lagrangian?
$endgroup$
– LinAlg
Jan 9 at 1:40
$begingroup$
why don't you have an objective function in your Lagrangian?
$endgroup$
– LinAlg
Jan 9 at 1:40
$begingroup$
@LinAlg i have added it
$endgroup$
– electronic component
Jan 9 at 4:28
$begingroup$
@LinAlg i have added it
$endgroup$
– electronic component
Jan 9 at 4:28
$begingroup$
The KKT conditions also include a stationarity condition (which is the derivative of L with respect to the original optimization variable) and a complementary slackness condition.
$endgroup$
– LinAlg
Jan 9 at 13:40
$begingroup$
The KKT conditions also include a stationarity condition (which is the derivative of L with respect to the original optimization variable) and a complementary slackness condition.
$endgroup$
– LinAlg
Jan 9 at 13:40
add a comment |
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$begingroup$
only if the original constraints were equality constraints to begin with
$endgroup$
– LinAlg
Jan 8 at 17:53
$begingroup$
yes!the formula to be zero is actually the original constraints were equality constraints,so is my thinking right?
$endgroup$
– electronic component
Jan 9 at 0:58
$begingroup$
why don't you have an objective function in your Lagrangian?
$endgroup$
– LinAlg
Jan 9 at 1:40
$begingroup$
@LinAlg i have added it
$endgroup$
– electronic component
Jan 9 at 4:28
$begingroup$
The KKT conditions also include a stationarity condition (which is the derivative of L with respect to the original optimization variable) and a complementary slackness condition.
$endgroup$
– LinAlg
Jan 9 at 13:40