Find tangent cone to closed convex set
$begingroup$
Let $X = {xinmathbb{R}^5: x_i geq 0, x_1+2x_2-x_3 = 6,x_1 + x_2 + 2x_4 -x_5 = 4}$, and I am looking to find the tangent cone to $X$ at the point $(0,4,2,0,0)$. How would I go about this?
I know that $X$ is closed and convex and therefore the tangent cone is just ${{a(y-(0,4,2,0,0)): y in X, a geq 0}}$, but I think because it is in five dimensions I am having trouble picturing it. One idea I had was to find the normal cone, i.e. ${v in mathbb{R}^5: langle v, x-(0,4,2,0,0)rangle leq 0 forall x in X}$, but I can't figure out how to do this either
calculus optimization convex-optimization
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
$endgroup$
add a comment |
$begingroup$
Let $X = {xinmathbb{R}^5: x_i geq 0, x_1+2x_2-x_3 = 6,x_1 + x_2 + 2x_4 -x_5 = 4}$, and I am looking to find the tangent cone to $X$ at the point $(0,4,2,0,0)$. How would I go about this?
I know that $X$ is closed and convex and therefore the tangent cone is just ${{a(y-(0,4,2,0,0)): y in X, a geq 0}}$, but I think because it is in five dimensions I am having trouble picturing it. One idea I had was to find the normal cone, i.e. ${v in mathbb{R}^5: langle v, x-(0,4,2,0,0)rangle leq 0 forall x in X}$, but I can't figure out how to do this either
calculus optimization convex-optimization
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
$endgroup$
add a comment |
$begingroup$
Let $X = {xinmathbb{R}^5: x_i geq 0, x_1+2x_2-x_3 = 6,x_1 + x_2 + 2x_4 -x_5 = 4}$, and I am looking to find the tangent cone to $X$ at the point $(0,4,2,0,0)$. How would I go about this?
I know that $X$ is closed and convex and therefore the tangent cone is just ${{a(y-(0,4,2,0,0)): y in X, a geq 0}}$, but I think because it is in five dimensions I am having trouble picturing it. One idea I had was to find the normal cone, i.e. ${v in mathbb{R}^5: langle v, x-(0,4,2,0,0)rangle leq 0 forall x in X}$, but I can't figure out how to do this either
calculus optimization convex-optimization
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
$endgroup$
Let $X = {xinmathbb{R}^5: x_i geq 0, x_1+2x_2-x_3 = 6,x_1 + x_2 + 2x_4 -x_5 = 4}$, and I am looking to find the tangent cone to $X$ at the point $(0,4,2,0,0)$. How would I go about this?
I know that $X$ is closed and convex and therefore the tangent cone is just ${{a(y-(0,4,2,0,0)): y in X, a geq 0}}$, but I think because it is in five dimensions I am having trouble picturing it. One idea I had was to find the normal cone, i.e. ${v in mathbb{R}^5: langle v, x-(0,4,2,0,0)rangle leq 0 forall x in X}$, but I can't figure out how to do this either
calculus optimization convex-optimization
calculus optimization convex-optimization
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
edited Dec 10 '18 at 18:43
John Smith
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
asked Dec 9 '18 at 20:55
John SmithJohn Smith
1448
1448
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%2f3032994%2ffind-tangent-cone-to-closed-convex-set%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%2f3032994%2ffind-tangent-cone-to-closed-convex-set%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
