prove that the functional is $alpha$-elliptic
0
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I got a nonlinear functional who is convex and Gâteaux differentiable. Is there some property of these two that can bring me that the functional is $alpha$-elliptic???
convex-analysis convex-optimization gateaux-derivative
asked Dec 3 '18 at 19:09
AndrewAndrew
336
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add a comment |
0
$begingroup$
I got a nonlinear functional who is convex and Gâteaux differentiable. Is there some property of these two that can bring me that the functional is $alpha$-elliptic???
convex-analysis convex-optimization gateaux-derivative
asked Dec 3 '18 at 19:09
AndrewAndrew
336
$endgroup$
$begingroup$
Can you define $alpha$-convex for us, please?
$endgroup$
– max_zorn
Dec 3 '18 at 20:05
$begingroup$
Sorry, I mean $alpha$-ellipticity $$biglangle J'left(uright)-J'left(vright),u-vbigranglegeqalpha|u-v|^2_{X},,;forall;u,vin X.$$
$endgroup$
– Andrew
Dec 3 '18 at 20:11
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Ah, strongly convex functions. Check the books by Borwein-Vanderwerff and by Zalinescu.
$endgroup$
– max_zorn
Dec 3 '18 at 20:18
$begingroup$
My functional is coercive, convex and Gateaux differentiable. This can't bring me some strong convexity? without the definition?
$endgroup$
– Andrew
Dec 4 '18 at 16:01
$begingroup$
Maybe not. Have you looked at $|x|^p$ for $1<p<+infty$?
$endgroup$
– max_zorn
Dec 5 '18 at 5:35
add a comment |
0
0
0
$begingroup$
I got a nonlinear functional who is convex and Gâteaux differentiable. Is there some property of these two that can bring me that the functional is $alpha$-elliptic???
convex-analysis convex-optimization gateaux-derivative
asked Dec 3 '18 at 19:09
AndrewAndrew
336
$endgroup$
I got a nonlinear functional who is convex and Gâteaux differentiable. Is there some property of these two that can bring me that the functional is $alpha$-elliptic???
convex-analysis convex-optimization gateaux-derivative
convex-analysis convex-optimization gateaux-derivative
asked Dec 3 '18 at 19:09
AndrewAndrew
336
asked Dec 3 '18 at 19:09
AndrewAndrew
336
edited Dec 3 '18 at 20:14
Andrew
asked Dec 3 '18 at 19:09
AndrewAndrew
336
asked Dec 3 '18 at 19:09
AndrewAndrew
336
asked Dec 3 '18 at 19:09
AndrewAndrew
336
336
$begingroup$
Can you define $alpha$-convex for us, please?
$endgroup$
– max_zorn
Dec 3 '18 at 20:05
$begingroup$
Sorry, I mean $alpha$-ellipticity $$biglangle J'left(uright)-J'left(vright),u-vbigranglegeqalpha|u-v|^2_{X},,;forall;u,vin X.$$
$endgroup$
– Andrew
Dec 3 '18 at 20:11
$begingroup$
Ah, strongly convex functions. Check the books by Borwein-Vanderwerff and by Zalinescu.
$endgroup$
– max_zorn
Dec 3 '18 at 20:18
$begingroup$
My functional is coercive, convex and Gateaux differentiable. This can't bring me some strong convexity? without the definition?
$endgroup$
– Andrew
Dec 4 '18 at 16:01
$begingroup$
Maybe not. Have you looked at $|x|^p$ for $1<p<+infty$?
$endgroup$
– max_zorn
Dec 5 '18 at 5:35
add a comment |
$begingroup$
Can you define $alpha$-convex for us, please?
$endgroup$
– max_zorn
Dec 3 '18 at 20:05
$begingroup$
Sorry, I mean $alpha$-ellipticity $$biglangle J'left(uright)-J'left(vright),u-vbigranglegeqalpha|u-v|^2_{X},,;forall;u,vin X.$$
$endgroup$
– Andrew
Dec 3 '18 at 20:11
$begingroup$
Ah, strongly convex functions. Check the books by Borwein-Vanderwerff and by Zalinescu.
$endgroup$
– max_zorn
Dec 3 '18 at 20:18
$begingroup$
My functional is coercive, convex and Gateaux differentiable. This can't bring me some strong convexity? without the definition?
$endgroup$
– Andrew
Dec 4 '18 at 16:01
$begingroup$
Maybe not. Have you looked at $|x|^p$ for $1<p<+infty$?
$endgroup$
– max_zorn
Dec 5 '18 at 5:35
$begingroup$
Can you define $alpha$-convex for us, please?
$endgroup$
– max_zorn
Dec 3 '18 at 20:05
$begingroup$
Can you define $alpha$-convex for us, please?
$endgroup$
– max_zorn
Dec 3 '18 at 20:05
$begingroup$
Sorry, I mean $alpha$-ellipticity $$biglangle J'left(uright)-J'left(vright),u-vbigranglegeqalpha|u-v|^2_{X},,;forall;u,vin X.$$
$endgroup$
– Andrew
Dec 3 '18 at 20:11
$begingroup$
Sorry, I mean $alpha$-ellipticity $$biglangle J'left(uright)-J'left(vright),u-vbigranglegeqalpha|u-v|^2_{X},,;forall;u,vin X.$$
$endgroup$
– Andrew
Dec 3 '18 at 20:11
$begingroup$
Ah, strongly convex functions. Check the books by Borwein-Vanderwerff and by Zalinescu.
$endgroup$
– max_zorn
Dec 3 '18 at 20:18
$begingroup$
Ah, strongly convex functions. Check the books by Borwein-Vanderwerff and by Zalinescu.
$endgroup$
– max_zorn
Dec 3 '18 at 20:18
$begingroup$
My functional is coercive, convex and Gateaux differentiable. This can't bring me some strong convexity? without the definition?
$endgroup$
– Andrew
Dec 4 '18 at 16:01
$begingroup$
My functional is coercive, convex and Gateaux differentiable. This can't bring me some strong convexity? without the definition?
$endgroup$
– Andrew
Dec 4 '18 at 16:01
$begingroup$
Maybe not. Have you looked at $|x|^p$ for $1<p<+infty$?
$endgroup$
– max_zorn
Dec 5 '18 at 5:35
$begingroup$
Maybe not. Have you looked at $|x|^p$ for $1<p<+infty$?
$endgroup$
– max_zorn
Dec 5 '18 at 5:35
add a comment |
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$begingroup$
Can you define $alpha$-convex for us, please?
$endgroup$
– max_zorn
Dec 3 '18 at 20:05
$begingroup$
Sorry, I mean $alpha$-ellipticity $$biglangle J'left(uright)-J'left(vright),u-vbigranglegeqalpha|u-v|^2_{X},,;forall;u,vin X.$$
$endgroup$
– Andrew
Dec 3 '18 at 20:11
$begingroup$
Ah, strongly convex functions. Check the books by Borwein-Vanderwerff and by Zalinescu.
$endgroup$
– max_zorn
Dec 3 '18 at 20:18
$begingroup$
My functional is coercive, convex and Gateaux differentiable. This can't bring me some strong convexity? without the definition?
$endgroup$
– Andrew
Dec 4 '18 at 16:01
$begingroup$
Maybe not. Have you looked at $|x|^p$ for $1<p<+infty$?
$endgroup$
– max_zorn
Dec 5 '18 at 5:35