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
328111
$endgroup$
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
328111
$endgroup$
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
328111
$endgroup$
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
328111
edited Jan 3 at 7:36
Saad
19.7k92352
asked Jan 3 at 7:16
LeeLee
328111
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
328111
asked Jan 3 at 7:16
LeeLee
328111
asked Jan 3 at 7:16
LeeLee
328111
328111
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3060323%2fmaximizing-fracx-11-dettt-22t-42-subject-to-txtt-ii-leq-p%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3060323%2fmaximizing-fracx-11-dettt-22t-42-subject-to-txtt-ii-leq-p%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
