convexity of the function f(x,y)=$int_{0}^{x^2+y^4} e^{t^2} dt $
0
$begingroup$
To study the convexity of this function I calculate the Hessian but is complicate to find is semi-definite positive or negative.
real-analysis
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
$endgroup$
add a comment |
0
$begingroup$
To study the convexity of this function I calculate the Hessian but is complicate to find is semi-definite positive or negative.
real-analysis
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
$endgroup$
$begingroup$
Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+y^4$ is convex. Now compose...
$endgroup$
– copper.hat
Jan 15 at 20:50
$begingroup$
@copper.hat Unfortunately the composition of convex functions can be nonconvex...
$endgroup$
– JRen
Jan 15 at 21:01
1
$begingroup$
@JRen: Fortunately the composition of a non decreasing convex function with a convex function is.
$endgroup$
– copper.hat
Jan 15 at 21:03
$begingroup$
@JRen: A moment's thought will show how to extend $g$ for $x <0$. (This is not the first time I have seen a convex function :-)).
$endgroup$
– copper.hat
Jan 15 at 21:07
$begingroup$
@copper.hat: Oh you'r right.
$endgroup$
– JRen
Jan 15 at 21:07
add a comment |
0
0
0
$begingroup$
To study the convexity of this function I calculate the Hessian but is complicate to find is semi-definite positive or negative.
real-analysis
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
$endgroup$
To study the convexity of this function I calculate the Hessian but is complicate to find is semi-definite positive or negative.
real-analysis
real-analysis
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
asked Jan 15 at 20:39
Giulia B.Giulia B.
512311
512311
$begingroup$
Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+y^4$ is convex. Now compose...
$endgroup$
– copper.hat
Jan 15 at 20:50
$begingroup$
@copper.hat Unfortunately the composition of convex functions can be nonconvex...
$endgroup$
– JRen
Jan 15 at 21:01
1
$begingroup$
@JRen: Fortunately the composition of a non decreasing convex function with a convex function is.
$endgroup$
– copper.hat
Jan 15 at 21:03
$begingroup$
@JRen: A moment's thought will show how to extend $g$ for $x <0$. (This is not the first time I have seen a convex function :-)).
$endgroup$
– copper.hat
Jan 15 at 21:07
$begingroup$
@copper.hat: Oh you'r right.
$endgroup$
– JRen
Jan 15 at 21:07
add a comment |
$begingroup$
Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+y^4$ is convex. Now compose...
$endgroup$
– copper.hat
Jan 15 at 20:50
$begingroup$
@copper.hat Unfortunately the composition of convex functions can be nonconvex...
$endgroup$
– JRen
Jan 15 at 21:01
1
$begingroup$
@JRen: Fortunately the composition of a non decreasing convex function with a convex function is.
$endgroup$
– copper.hat
Jan 15 at 21:03
$begingroup$
@JRen: A moment's thought will show how to extend $g$ for $x <0$. (This is not the first time I have seen a convex function :-)).
$endgroup$
– copper.hat
Jan 15 at 21:07
$begingroup$
@copper.hat: Oh you'r right.
$endgroup$
– JRen
Jan 15 at 21:07
$begingroup$
Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+y^4$ is convex. Now compose...
$endgroup$
– copper.hat
Jan 15 at 20:50
$begingroup$
Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+y^4$ is convex. Now compose...
$endgroup$
– copper.hat
Jan 15 at 20:50
$begingroup$
@copper.hat Unfortunately the composition of convex functions can be nonconvex...
$endgroup$
– JRen
Jan 15 at 21:01
$begingroup$
@copper.hat Unfortunately the composition of convex functions can be nonconvex...
$endgroup$
– JRen
Jan 15 at 21:01
1
1
$begingroup$
@JRen: Fortunately the composition of a non decreasing convex function with a convex function is.
$endgroup$
– copper.hat
Jan 15 at 21:03
$begingroup$
@JRen: Fortunately the composition of a non decreasing convex function with a convex function is.
$endgroup$
– copper.hat
Jan 15 at 21:03
$begingroup$
@JRen: A moment's thought will show how to extend $g$ for $x <0$. (This is not the first time I have seen a convex function :-)).
$endgroup$
– copper.hat
Jan 15 at 21:07
$begingroup$
@JRen: A moment's thought will show how to extend $g$ for $x <0$. (This is not the first time I have seen a convex function :-)).
$endgroup$
– copper.hat
Jan 15 at 21:07
$begingroup$
@copper.hat: Oh you'r right.
$endgroup$
– JRen
Jan 15 at 21:07
$begingroup$
@copper.hat: Oh you'r right.
$endgroup$
– JRen
Jan 15 at 21:07
add a comment |
0
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$begingroup$
Let $g(x) = int_0^x e^{t^2} dt $ for $x ge 0$. It is convex and increasing. The function $(x,y) mapsto x^2+y^4$ is convex. Now compose...
$endgroup$
– copper.hat
Jan 15 at 20:50
$begingroup$
@copper.hat Unfortunately the composition of convex functions can be nonconvex...
$endgroup$
– JRen
Jan 15 at 21:01
1
$begingroup$
@JRen: Fortunately the composition of a non decreasing convex function with a convex function is.
$endgroup$
– copper.hat
Jan 15 at 21:03
$begingroup$
@JRen: A moment's thought will show how to extend $g$ for $x <0$. (This is not the first time I have seen a convex function :-)).
$endgroup$
– copper.hat
Jan 15 at 21:07
$begingroup$
@copper.hat: Oh you'r right.
$endgroup$
– JRen
Jan 15 at 21:07