Is the product of L2 norm and L-infinity norm convex?
0
$begingroup$
Let $x in mathbb{R}^n$ be an vector, and $f(x) = ||x||_2 cdot ||x||_infty$, I was wondering if $f(x)$ is a convex function?
Thanks!
optimization norm
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
$endgroup$
add a comment |
0
$begingroup$
Let $x in mathbb{R}^n$ be an vector, and $f(x) = ||x||_2 cdot ||x||_infty$, I was wondering if $f(x)$ is a convex function?
Thanks!
optimization norm
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
$endgroup$
$begingroup$
Could you give some context? Why is this question interesting? Have you tried anything? Also it is not clear what $x$ is.
$endgroup$
– Michh
Dec 28 '18 at 21:04
$begingroup$
- No, it isn't.
$endgroup$
– A.Γ.
Dec 28 '18 at 21:24
$begingroup$
@Michh $x$ is a vector, I have edited my question.
$endgroup$
– user3138073
Dec 28 '18 at 22:20
$begingroup$
@A.Γ.thanks for the answer, but could you tell me why?
$endgroup$
– user3138073
Dec 28 '18 at 22:22
$begingroup$
One can find a counterexample: $x,yinBbb{R}^n$ (with some large enough $n$) and $lambdain[0,1]$ such that $f(lambda x+(1-lambda)y)>lambda f(x)+(1-lambda)f(y)$.
$endgroup$
– A.Γ.
Dec 29 '18 at 10:07
add a comment |
0
0
0
$begingroup$
Let $x in mathbb{R}^n$ be an vector, and $f(x) = ||x||_2 cdot ||x||_infty$, I was wondering if $f(x)$ is a convex function?
Thanks!
optimization norm
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
$endgroup$
Let $x in mathbb{R}^n$ be an vector, and $f(x) = ||x||_2 cdot ||x||_infty$, I was wondering if $f(x)$ is a convex function?
Thanks!
optimization norm
optimization norm
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
edited Dec 28 '18 at 22:20
user3138073
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
asked Dec 28 '18 at 8:39
user3138073user3138073
1908
1908
$begingroup$
Could you give some context? Why is this question interesting? Have you tried anything? Also it is not clear what $x$ is.
$endgroup$
– Michh
Dec 28 '18 at 21:04
$begingroup$
- No, it isn't.
$endgroup$
– A.Γ.
Dec 28 '18 at 21:24
$begingroup$
@Michh $x$ is a vector, I have edited my question.
$endgroup$
– user3138073
Dec 28 '18 at 22:20
$begingroup$
@A.Γ.thanks for the answer, but could you tell me why?
$endgroup$
– user3138073
Dec 28 '18 at 22:22
$begingroup$
One can find a counterexample: $x,yinBbb{R}^n$ (with some large enough $n$) and $lambdain[0,1]$ such that $f(lambda x+(1-lambda)y)>lambda f(x)+(1-lambda)f(y)$.
$endgroup$
– A.Γ.
Dec 29 '18 at 10:07
add a comment |
$begingroup$
Could you give some context? Why is this question interesting? Have you tried anything? Also it is not clear what $x$ is.
$endgroup$
– Michh
Dec 28 '18 at 21:04
$begingroup$
- No, it isn't.
$endgroup$
– A.Γ.
Dec 28 '18 at 21:24
$begingroup$
@Michh $x$ is a vector, I have edited my question.
$endgroup$
– user3138073
Dec 28 '18 at 22:20
$begingroup$
@A.Γ.thanks for the answer, but could you tell me why?
$endgroup$
– user3138073
Dec 28 '18 at 22:22
$begingroup$
One can find a counterexample: $x,yinBbb{R}^n$ (with some large enough $n$) and $lambdain[0,1]$ such that $f(lambda x+(1-lambda)y)>lambda f(x)+(1-lambda)f(y)$.
$endgroup$
– A.Γ.
Dec 29 '18 at 10:07
$begingroup$
Could you give some context? Why is this question interesting? Have you tried anything? Also it is not clear what $x$ is.
$endgroup$
– Michh
Dec 28 '18 at 21:04
$begingroup$
Could you give some context? Why is this question interesting? Have you tried anything? Also it is not clear what $x$ is.
$endgroup$
– Michh
Dec 28 '18 at 21:04
$begingroup$
- No, it isn't.
$endgroup$
– A.Γ.
Dec 28 '18 at 21:24
$begingroup$
- No, it isn't.
$endgroup$
– A.Γ.
Dec 28 '18 at 21:24
$begingroup$
@Michh $x$ is a vector, I have edited my question.
$endgroup$
– user3138073
Dec 28 '18 at 22:20
$begingroup$
@Michh $x$ is a vector, I have edited my question.
$endgroup$
– user3138073
Dec 28 '18 at 22:20
$begingroup$
@A.Γ.thanks for the answer, but could you tell me why?
$endgroup$
– user3138073
Dec 28 '18 at 22:22
$begingroup$
@A.Γ.thanks for the answer, but could you tell me why?
$endgroup$
– user3138073
Dec 28 '18 at 22:22
$begingroup$
One can find a counterexample: $x,yinBbb{R}^n$ (with some large enough $n$) and $lambdain[0,1]$ such that $f(lambda x+(1-lambda)y)>lambda f(x)+(1-lambda)f(y)$.
$endgroup$
– A.Γ.
Dec 29 '18 at 10:07
$begingroup$
One can find a counterexample: $x,yinBbb{R}^n$ (with some large enough $n$) and $lambdain[0,1]$ such that $f(lambda x+(1-lambda)y)>lambda f(x)+(1-lambda)f(y)$.
$endgroup$
– A.Γ.
Dec 29 '18 at 10:07
add a comment |
0
active
oldest
votes
Your Answer
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
});
}
});
draft saved
draft discarded
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%2f3054685%2fis-the-product-of-l2-norm-and-l-infinity-norm-convex%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
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3054685%2fis-the-product-of-l2-norm-and-l-infinity-norm-convex%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
$begingroup$
Could you give some context? Why is this question interesting? Have you tried anything? Also it is not clear what $x$ is.
$endgroup$
– Michh
Dec 28 '18 at 21:04
$begingroup$
- No, it isn't.
$endgroup$
– A.Γ.
Dec 28 '18 at 21:24
$begingroup$
@Michh $x$ is a vector, I have edited my question.
$endgroup$
– user3138073
Dec 28 '18 at 22:20
$begingroup$
@A.Γ.thanks for the answer, but could you tell me why?
$endgroup$
– user3138073
Dec 28 '18 at 22:22
$begingroup$
One can find a counterexample: $x,yinBbb{R}^n$ (with some large enough $n$) and $lambdain[0,1]$ such that $f(lambda x+(1-lambda)y)>lambda f(x)+(1-lambda)f(y)$.
$endgroup$
– A.Γ.
Dec 29 '18 at 10:07