How do I optimize Ax = b such that every element of b is bigger than 0.5 and x has the lowest possible norm?
$begingroup$
As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.
A is a symmetric definite positive matrix
Thanks!!
matrices optimization matrix-equations
$endgroup$
add a comment |
$begingroup$
As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.
A is a symmetric definite positive matrix
Thanks!!
matrices optimization matrix-equations
$endgroup$
$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08
$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36
$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51
$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54
add a comment |
$begingroup$
As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.
A is a symmetric definite positive matrix
Thanks!!
matrices optimization matrix-equations
$endgroup$
As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.
A is a symmetric definite positive matrix
Thanks!!
matrices optimization matrix-equations
matrices optimization matrix-equations
asked Jan 1 at 18:01
MichaelMichael
444
444
$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08
$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36
$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51
$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54
add a comment |
$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08
$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36
$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51
$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54
$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08
$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08
$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36
$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36
$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51
$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51
$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54
$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54
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%2f3058703%2fhow-do-i-optimize-ax-b-such-that-every-element-of-b-is-bigger-than-0-5-and-x-h%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%2f3058703%2fhow-do-i-optimize-ax-b-such-that-every-element-of-b-is-bigger-than-0-5-and-x-h%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
$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08
$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36
$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51
$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54