Mixing
Maximizing $frac{X_{11}det(T)}{T_2^2+T_4^2}$ subject to ${TXT^T}_{ii}leq P_i$
$begingroup$
begin{array}{ll} text{maximize} & frac{X_{11}det(T)}{T_2^2+T_4^2}\ text{subject to} & {TXT^T}_{ii}leq P_iend{array}
where $Tinmathbb{R^{2times2}}$, $T=begin{bmatrix}T_1 & T_2\T_3 &T_4end{bmatrix}$, $T$ is invertible, $Xinmathbb{R^{2times2}}$, $X=begin{bmatrix}X_{11} & X_{12}\X_{12} &X_{22}end{bmatrix}>0$ (positive definite).
We need to maximize in terms of $P_1$ and $P_2$, which are given. I have no idea how to tackle this question, even when $T$ is unitary, we just need to maximize $X_{11}$, it turns out not straightforward.
matrices optimization
edited Jan 3 at 7:36
Saad
19.7k92352
asked Jan 3 at 7:16
LeeLee
332111
$endgroup$
add a comment |
$begingroup$
begin{array}{ll} text{maximize} & frac{X_{11}det(T)}{T_2^2+T_4^2}\ text{subject to} & {TXT^T}_{ii}leq P_iend{array}
where $Tinmathbb{R^{2times2}}$, $T=begin{bmatrix}T_1 & T_2\T_3 &T_4end{bmatrix}$, $T$ is invertible, $Xinmathbb{R^{2times2}}$, $X=begin{bmatrix}X_{11} & X_{12}\X_{12} &X_{22}end{bmatrix}>0$ (positive definite).
We need to maximize in terms of $P_1$ and $P_2$, which are given. I have no idea how to tackle this question, even when $T$ is unitary, we just need to maximize $X_{11}$, it turns out not straightforward.
matrices optimization
edited Jan 3 at 7:36
Saad
19.7k92352
asked Jan 3 at 7:16
LeeLee
332111
$endgroup$
add a comment |
$begingroup$
begin{array}{ll} text{maximize} & frac{X_{11}det(T)}{T_2^2+T_4^2}\ text{subject to} & {TXT^T}_{ii}leq P_iend{array}
where $Tinmathbb{R^{2times2}}$, $T=begin{bmatrix}T_1 & T_2\T_3 &T_4end{bmatrix}$, $T$ is invertible, $Xinmathbb{R^{2times2}}$, $X=begin{bmatrix}X_{11} & X_{12}\X_{12} &X_{22}end{bmatrix}>0$ (positive definite).
We need to maximize in terms of $P_1$ and $P_2$, which are given. I have no idea how to tackle this question, even when $T$ is unitary, we just need to maximize $X_{11}$, it turns out not straightforward.
matrices optimization
edited Jan 3 at 7:36
Saad
19.7k92352
asked Jan 3 at 7:16
LeeLee
332111
$endgroup$
begin{array}{ll} text{maximize} & frac{X_{11}det(T)}{T_2^2+T_4^2}\ text{subject to} & {TXT^T}_{ii}leq P_iend{array}
where $Tinmathbb{R^{2times2}}$, $T=begin{bmatrix}T_1 & T_2\T_3 &T_4end{bmatrix}$, $T$ is invertible, $Xinmathbb{R^{2times2}}$, $X=begin{bmatrix}X_{11} & X_{12}\X_{12} &X_{22}end{bmatrix}>0$ (positive definite).
We need to maximize in terms of $P_1$ and $P_2$, which are given. I have no idea how to tackle this question, even when $T$ is unitary, we just need to maximize $X_{11}$, it turns out not straightforward.
matrices optimization
matrices optimization
edited Jan 3 at 7:36
Saad
19.7k92352
asked Jan 3 at 7:16
LeeLee
332111
edited Jan 3 at 7:36
Saad
19.7k92352
asked Jan 3 at 7:16
LeeLee
332111
edited Jan 3 at 7:36
Saad
19.7k92352
edited Jan 3 at 7:36
Saad
19.7k92352
edited Jan 3 at 7:36
Saad
19.7k92352
19.7k92352
asked Jan 3 at 7:16
LeeLee
332111
asked Jan 3 at 7:16
LeeLee
332111
asked Jan 3 at 7:16
LeeLee
332111
332111
add a comment |
add a comment |
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