(Worst and average case) Arithmetic and time complexity of a quadratic programming problem by interior point...
$begingroup$
My understanding of complexity measures are at basic level. So, please excuse me for asking basic question, if it sounds like.
I am trying to understand the arithmetic and time complexity of a following convex quadratically constrained problem.
$$min_{mathbf{X} in mathbb{C}^{N times K}} left|mathbf{Y}-mathbf{X}right|_F^2 hspace{5mm} {rm s.t.} left|mathbf{A}mathbf{X}^Tright|^2 leq mathbf{B} ,$$
where inequality is component wise, $mathbf{A} in mathbb{C}^{M times K}$, and $mathbf{B} in mathbb{R}^{M times N}$.
For instance here I see that they comment such QCQP porblem (similar to my case?) has polynomial time complexity (but still I fail to put it in numbers :( ... this is probably my problem)
computer-science computational-complexity numerical-linear-algebra nonlinear-optimization numerical-optimization
asked Nov 27 '18 at 10:58
learninglearning
516
$endgroup$
add a comment |
$begingroup$
My understanding of complexity measures are at basic level. So, please excuse me for asking basic question, if it sounds like.
I am trying to understand the arithmetic and time complexity of a following convex quadratically constrained problem.
$$min_{mathbf{X} in mathbb{C}^{N times K}} left|mathbf{Y}-mathbf{X}right|_F^2 hspace{5mm} {rm s.t.} left|mathbf{A}mathbf{X}^Tright|^2 leq mathbf{B} ,$$
where inequality is component wise, $mathbf{A} in mathbb{C}^{M times K}$, and $mathbf{B} in mathbb{R}^{M times N}$.
For instance here I see that they comment such QCQP porblem (similar to my case?) has polynomial time complexity (but still I fail to put it in numbers :( ... this is probably my problem)
computer-science computational-complexity numerical-linear-algebra nonlinear-optimization numerical-optimization
asked Nov 27 '18 at 10:58
learninglearning
516
$endgroup$
add a comment |
$begingroup$
My understanding of complexity measures are at basic level. So, please excuse me for asking basic question, if it sounds like.
I am trying to understand the arithmetic and time complexity of a following convex quadratically constrained problem.
$$min_{mathbf{X} in mathbb{C}^{N times K}} left|mathbf{Y}-mathbf{X}right|_F^2 hspace{5mm} {rm s.t.} left|mathbf{A}mathbf{X}^Tright|^2 leq mathbf{B} ,$$
where inequality is component wise, $mathbf{A} in mathbb{C}^{M times K}$, and $mathbf{B} in mathbb{R}^{M times N}$.
For instance here I see that they comment such QCQP porblem (similar to my case?) has polynomial time complexity (but still I fail to put it in numbers :( ... this is probably my problem)
computer-science computational-complexity numerical-linear-algebra nonlinear-optimization numerical-optimization
asked Nov 27 '18 at 10:58
learninglearning
516
$endgroup$
My understanding of complexity measures are at basic level. So, please excuse me for asking basic question, if it sounds like.
I am trying to understand the arithmetic and time complexity of a following convex quadratically constrained problem.
$$min_{mathbf{X} in mathbb{C}^{N times K}} left|mathbf{Y}-mathbf{X}right|_F^2 hspace{5mm} {rm s.t.} left|mathbf{A}mathbf{X}^Tright|^2 leq mathbf{B} ,$$
where inequality is component wise, $mathbf{A} in mathbb{C}^{M times K}$, and $mathbf{B} in mathbb{R}^{M times N}$.
For instance here I see that they comment such QCQP porblem (similar to my case?) has polynomial time complexity (but still I fail to put it in numbers :( ... this is probably my problem)
computer-science computational-complexity numerical-linear-algebra nonlinear-optimization numerical-optimization
computer-science computational-complexity numerical-linear-algebra nonlinear-optimization numerical-optimization
asked Nov 27 '18 at 10:58
learninglearning
516
asked Nov 27 '18 at 10:58
learninglearning
516
asked Nov 27 '18 at 10:58
learninglearning
516
asked Nov 27 '18 at 10:58
learninglearning
516
asked Nov 27 '18 at 10:58
learninglearning
516
516
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%2f3015647%2fworst-and-average-case-arithmetic-and-time-complexity-of-a-quadratic-programmi%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%2f3015647%2fworst-and-average-case-arithmetic-and-time-complexity-of-a-quadratic-programmi%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
