Strongly convexity of a nonlinear functional
0
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I got the following nonlinear functional
$$Jleft(uright)=frac{1}{2}int_{Omega}left[Hleft(nabla uright)right]^2;dx-int_{Omega}fcdot u;dx,;forall;vin X$$,
where $H$ is a Finsler norm, who is convex.
How to prove that this functional is strongly convex?
functional-analysis convex-analysis convex-optimization
asked Dec 3 '18 at 19:57
AndrewAndrew
346
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add a comment |
0
$begingroup$
I got the following nonlinear functional
$$Jleft(uright)=frac{1}{2}int_{Omega}left[Hleft(nabla uright)right]^2;dx-int_{Omega}fcdot u;dx,;forall;vin X$$,
where $H$ is a Finsler norm, who is convex.
How to prove that this functional is strongly convex?
functional-analysis convex-analysis convex-optimization
asked Dec 3 '18 at 19:57
AndrewAndrew
346
$endgroup$
$begingroup$
This functional is linear on constant functions, so not strongly convex without further assumptions. What is $X$? Is $H$ strongly convex?
$endgroup$
– daw
Dec 3 '18 at 20:24
$begingroup$
$H$ is just a norm who is convex and homogeneous of degree 1, but not linear. I don't know if it is strongly convex. X is just a Hilbert space.
$endgroup$
– Andrew
Dec 3 '18 at 20:29
add a comment |
0
0
0
$begingroup$
I got the following nonlinear functional
$$Jleft(uright)=frac{1}{2}int_{Omega}left[Hleft(nabla uright)right]^2;dx-int_{Omega}fcdot u;dx,;forall;vin X$$,
where $H$ is a Finsler norm, who is convex.
How to prove that this functional is strongly convex?
functional-analysis convex-analysis convex-optimization
asked Dec 3 '18 at 19:57
AndrewAndrew
346
$endgroup$
I got the following nonlinear functional
$$Jleft(uright)=frac{1}{2}int_{Omega}left[Hleft(nabla uright)right]^2;dx-int_{Omega}fcdot u;dx,;forall;vin X$$,
where $H$ is a Finsler norm, who is convex.
How to prove that this functional is strongly convex?
functional-analysis convex-analysis convex-optimization
functional-analysis convex-analysis convex-optimization
asked Dec 3 '18 at 19:57
AndrewAndrew
346
asked Dec 3 '18 at 19:57
AndrewAndrew
346
asked Dec 3 '18 at 19:57
AndrewAndrew
346
asked Dec 3 '18 at 19:57
AndrewAndrew
346
asked Dec 3 '18 at 19:57
AndrewAndrew
346
346
$begingroup$
This functional is linear on constant functions, so not strongly convex without further assumptions. What is $X$? Is $H$ strongly convex?
$endgroup$
– daw
Dec 3 '18 at 20:24
$begingroup$
$H$ is just a norm who is convex and homogeneous of degree 1, but not linear. I don't know if it is strongly convex. X is just a Hilbert space.
$endgroup$
– Andrew
Dec 3 '18 at 20:29
add a comment |
$begingroup$
This functional is linear on constant functions, so not strongly convex without further assumptions. What is $X$? Is $H$ strongly convex?
$endgroup$
– daw
Dec 3 '18 at 20:24
$begingroup$
$H$ is just a norm who is convex and homogeneous of degree 1, but not linear. I don't know if it is strongly convex. X is just a Hilbert space.
$endgroup$
– Andrew
Dec 3 '18 at 20:29
$begingroup$
This functional is linear on constant functions, so not strongly convex without further assumptions. What is $X$? Is $H$ strongly convex?
$endgroup$
– daw
Dec 3 '18 at 20:24
$begingroup$
This functional is linear on constant functions, so not strongly convex without further assumptions. What is $X$? Is $H$ strongly convex?
$endgroup$
– daw
Dec 3 '18 at 20:24
$begingroup$
$H$ is just a norm who is convex and homogeneous of degree 1, but not linear. I don't know if it is strongly convex. X is just a Hilbert space.
$endgroup$
– Andrew
Dec 3 '18 at 20:29
$begingroup$
$H$ is just a norm who is convex and homogeneous of degree 1, but not linear. I don't know if it is strongly convex. X is just a Hilbert space.
$endgroup$
– Andrew
Dec 3 '18 at 20:29
add a comment |
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$begingroup$
This functional is linear on constant functions, so not strongly convex without further assumptions. What is $X$? Is $H$ strongly convex?
$endgroup$
– daw
Dec 3 '18 at 20:24
$begingroup$
$H$ is just a norm who is convex and homogeneous of degree 1, but not linear. I don't know if it is strongly convex. X is just a Hilbert space.
$endgroup$
– Andrew
Dec 3 '18 at 20:29