Optimum of a multivariate polynomial over an interval

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












I'm looking for a way to minimize (or maximize) the following quadratic form : $aX^2 + bY^2 + cXY$ with the coefficients $ (a, b, c) in mathbbR^3$, subject to constraints $(X, Y) in [X_-, X_+] times [Y_-,Y_+]$



Are there fast ways to solve for $(X, Y)$ that realizes the optimum value ? (possibly Analytic ?)



Thanks







share|cite|improve this question




















  • Can you please re-write the question in a clearer way?
    – aslv95
    Aug 26 at 19:43














up vote
0
down vote

favorite












I'm looking for a way to minimize (or maximize) the following quadratic form : $aX^2 + bY^2 + cXY$ with the coefficients $ (a, b, c) in mathbbR^3$, subject to constraints $(X, Y) in [X_-, X_+] times [Y_-,Y_+]$



Are there fast ways to solve for $(X, Y)$ that realizes the optimum value ? (possibly Analytic ?)



Thanks







share|cite|improve this question




















  • Can you please re-write the question in a clearer way?
    – aslv95
    Aug 26 at 19:43












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I'm looking for a way to minimize (or maximize) the following quadratic form : $aX^2 + bY^2 + cXY$ with the coefficients $ (a, b, c) in mathbbR^3$, subject to constraints $(X, Y) in [X_-, X_+] times [Y_-,Y_+]$



Are there fast ways to solve for $(X, Y)$ that realizes the optimum value ? (possibly Analytic ?)



Thanks







share|cite|improve this question












I'm looking for a way to minimize (or maximize) the following quadratic form : $aX^2 + bY^2 + cXY$ with the coefficients $ (a, b, c) in mathbbR^3$, subject to constraints $(X, Y) in [X_-, X_+] times [Y_-,Y_+]$



Are there fast ways to solve for $(X, Y)$ that realizes the optimum value ? (possibly Analytic ?)



Thanks









share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 26 at 11:54









user3821901

112




112











  • Can you please re-write the question in a clearer way?
    – aslv95
    Aug 26 at 19:43
















  • Can you please re-write the question in a clearer way?
    – aslv95
    Aug 26 at 19:43















Can you please re-write the question in a clearer way?
– aslv95
Aug 26 at 19:43




Can you please re-write the question in a clearer way?
– aslv95
Aug 26 at 19:43















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',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2894964%2foptimum-of-a-multivariate-polynomial-over-an-interval%23new-answer', 'question_page');

);

Post as a guest



































active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2894964%2foptimum-of-a-multivariate-polynomial-over-an-interval%23new-answer', 'question_page');

);

Post as a guest













































































這個網誌中的熱門文章

How to combine Bézier curves to a surface?

Mutual Information Always Non-negative

Why am i infinitely getting the same tweet with the Twitter Search API?