Mixing
Is this function strictly convex and why?
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Is this function strictly convex?
$(x_1+x_2+x_3+x_4+x_5+x_6-30)^2+(x_7+x_8+x_9+x_{10}+x_{11}-24)^2+(x_1+x_7+x_8+x_4-14)^2$
variables are $x_i$ and we have $1 le x_i le 9$.
convex-analysis
asked Jan 21 at 21:01
Math-fortMath-fort
255
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show 4 more comments
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Is this function strictly convex?
$(x_1+x_2+x_3+x_4+x_5+x_6-30)^2+(x_7+x_8+x_9+x_{10}+x_{11}-24)^2+(x_1+x_7+x_8+x_4-14)^2$
variables are $x_i$ and we have $1 le x_i le 9$.
convex-analysis
asked Jan 21 at 21:01
Math-fortMath-fort
255
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Can you change it to MathJax/Latex?
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– Will M.
Jan 21 at 21:07
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Done..........!
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– Math-fort
Jan 21 at 21:11
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It should be clear that the answer is no: a strictly convex function can be at most a unique minimiser but this function has plenty.
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– Will M.
Jan 21 at 21:37
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I forgot to add the constraint $1 le x_i le 9$.
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– Math-fort
Jan 21 at 21:48
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But it is a sum of x^2 functions which are strictly convex!
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– Math-fort
Jan 21 at 21:48
|
show 4 more comments
$begingroup$
Is this function strictly convex?
$(x_1+x_2+x_3+x_4+x_5+x_6-30)^2+(x_7+x_8+x_9+x_{10}+x_{11}-24)^2+(x_1+x_7+x_8+x_4-14)^2$
variables are $x_i$ and we have $1 le x_i le 9$.
convex-analysis
asked Jan 21 at 21:01
Math-fortMath-fort
255
$endgroup$
Is this function strictly convex?
$(x_1+x_2+x_3+x_4+x_5+x_6-30)^2+(x_7+x_8+x_9+x_{10}+x_{11}-24)^2+(x_1+x_7+x_8+x_4-14)^2$
variables are $x_i$ and we have $1 le x_i le 9$.
convex-analysis
convex-analysis
asked Jan 21 at 21:01
Math-fortMath-fort
255
asked Jan 21 at 21:01
Math-fortMath-fort
255
edited Jan 21 at 21:47
Math-fort
asked Jan 21 at 21:01
Math-fortMath-fort
255
asked Jan 21 at 21:01
Math-fortMath-fort
255
asked Jan 21 at 21:01
Math-fortMath-fort
255
255
$begingroup$
Can you change it to MathJax/Latex?
$endgroup$
– Will M.
Jan 21 at 21:07
$begingroup$
Done..........!
$endgroup$
– Math-fort
Jan 21 at 21:11
$begingroup$
It should be clear that the answer is no: a strictly convex function can be at most a unique minimiser but this function has plenty.
$endgroup$
– Will M.
Jan 21 at 21:37
$begingroup$
I forgot to add the constraint $1 le x_i le 9$.
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
But it is a sum of x^2 functions which are strictly convex!
$endgroup$
– Math-fort
Jan 21 at 21:48
|
show 4 more comments
$begingroup$
Can you change it to MathJax/Latex?
$endgroup$
– Will M.
Jan 21 at 21:07
$begingroup$
Done..........!
$endgroup$
– Math-fort
Jan 21 at 21:11
$begingroup$
It should be clear that the answer is no: a strictly convex function can be at most a unique minimiser but this function has plenty.
$endgroup$
– Will M.
Jan 21 at 21:37
$begingroup$
I forgot to add the constraint $1 le x_i le 9$.
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
But it is a sum of x^2 functions which are strictly convex!
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
Can you change it to MathJax/Latex?
$endgroup$
– Will M.
Jan 21 at 21:07
$begingroup$
Can you change it to MathJax/Latex?
$endgroup$
– Will M.
Jan 21 at 21:07
$begingroup$
Done..........!
$endgroup$
– Math-fort
Jan 21 at 21:11
$begingroup$
Done..........!
$endgroup$
– Math-fort
Jan 21 at 21:11
$begingroup$
It should be clear that the answer is no: a strictly convex function can be at most a unique minimiser but this function has plenty.
$endgroup$
– Will M.
Jan 21 at 21:37
$begingroup$
It should be clear that the answer is no: a strictly convex function can be at most a unique minimiser but this function has plenty.
$endgroup$
– Will M.
Jan 21 at 21:37
$begingroup$
I forgot to add the constraint $1 le x_i le 9$.
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
I forgot to add the constraint $1 le x_i le 9$.
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
But it is a sum of x^2 functions which are strictly convex!
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
But it is a sum of x^2 functions which are strictly convex!
$endgroup$
– Math-fort
Jan 21 at 21:48
|
show 4 more comments
1 Answer
1
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Hint: fix all variables but $x_2$ and $x_3$ and have a look at the two-dimensional function (depending only on $x_2$ and $x_3$.
Note that a sum of squares is not always strictly convex, i.e., $(x_1,x_2) mapsto x_1^2$.
answered Jan 22 at 6:44
gerwgerw
19.6k11334
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint: fix all variables but $x_2$ and $x_3$ and have a look at the two-dimensional function (depending only on $x_2$ and $x_3$.
Note that a sum of squares is not always strictly convex, i.e., $(x_1,x_2) mapsto x_1^2$.
answered Jan 22 at 6:44
gerwgerw
19.6k11334
$endgroup$
add a comment |
$begingroup$
Hint: fix all variables but $x_2$ and $x_3$ and have a look at the two-dimensional function (depending only on $x_2$ and $x_3$.
Note that a sum of squares is not always strictly convex, i.e., $(x_1,x_2) mapsto x_1^2$.
answered Jan 22 at 6:44
gerwgerw
19.6k11334
$endgroup$
add a comment |
$begingroup$
Hint: fix all variables but $x_2$ and $x_3$ and have a look at the two-dimensional function (depending only on $x_2$ and $x_3$.
Note that a sum of squares is not always strictly convex, i.e., $(x_1,x_2) mapsto x_1^2$.
answered Jan 22 at 6:44
gerwgerw
19.6k11334
$endgroup$
Hint: fix all variables but $x_2$ and $x_3$ and have a look at the two-dimensional function (depending only on $x_2$ and $x_3$.
Note that a sum of squares is not always strictly convex, i.e., $(x_1,x_2) mapsto x_1^2$.
answered Jan 22 at 6:44
gerwgerw
19.6k11334
answered Jan 22 at 6:44
gerwgerw
19.6k11334
answered Jan 22 at 6:44
gerwgerw
19.6k11334
answered Jan 22 at 6:44
gerwgerw
19.6k11334
19.6k11334
add a comment |
add a comment |
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$begingroup$
Can you change it to MathJax/Latex?
$endgroup$
– Will M.
Jan 21 at 21:07
$begingroup$
Done..........!
$endgroup$
– Math-fort
Jan 21 at 21:11
$begingroup$
It should be clear that the answer is no: a strictly convex function can be at most a unique minimiser but this function has plenty.
$endgroup$
– Will M.
Jan 21 at 21:37
$begingroup$
I forgot to add the constraint $1 le x_i le 9$.
$endgroup$
– Math-fort
Jan 21 at 21:48
$begingroup$
But it is a sum of x^2 functions which are strictly convex!
$endgroup$
– Math-fort
Jan 21 at 21:48