Lagrangian multiplier based on calculus of variation
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The equation (6) and (7) on the chapter 3.2 in http://wnzhang.net/papers/ortb-kdd.pdf , there is Lagrange-multiplier based on calculus of variation.
I'm not sure that (7) is derived from (6).
As i think,
$F(theta, b(theta), b'(theta))$ = $theta w(b(theta))p_theta(theta) - lambda (b(theta)w(b(theta))p_theta(theta))$.
As Euler-Lagrange condition $fracpartial Fpartial b(theta) - fracddthetafracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)] - fracddthetafracpartial Fpartial b'(theta)=0$.
In last term $fracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)]=0$
Is it correct?
calculus-of-variations lagrange-multiplier euler-lagrange-equation
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The equation (6) and (7) on the chapter 3.2 in http://wnzhang.net/papers/ortb-kdd.pdf , there is Lagrange-multiplier based on calculus of variation.
I'm not sure that (7) is derived from (6).
As i think,
$F(theta, b(theta), b'(theta))$ = $theta w(b(theta))p_theta(theta) - lambda (b(theta)w(b(theta))p_theta(theta))$.
As Euler-Lagrange condition $fracpartial Fpartial b(theta) - fracddthetafracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)] - fracddthetafracpartial Fpartial b'(theta)=0$.
In last term $fracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)]=0$
Is it correct?
calculus-of-variations lagrange-multiplier euler-lagrange-equation
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
The equation (6) and (7) on the chapter 3.2 in http://wnzhang.net/papers/ortb-kdd.pdf , there is Lagrange-multiplier based on calculus of variation.
I'm not sure that (7) is derived from (6).
As i think,
$F(theta, b(theta), b'(theta))$ = $theta w(b(theta))p_theta(theta) - lambda (b(theta)w(b(theta))p_theta(theta))$.
As Euler-Lagrange condition $fracpartial Fpartial b(theta) - fracddthetafracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)] - fracddthetafracpartial Fpartial b'(theta)=0$.
In last term $fracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)]=0$
Is it correct?
calculus-of-variations lagrange-multiplier euler-lagrange-equation
The equation (6) and (7) on the chapter 3.2 in http://wnzhang.net/papers/ortb-kdd.pdf , there is Lagrange-multiplier based on calculus of variation.
I'm not sure that (7) is derived from (6).
As i think,
$F(theta, b(theta), b'(theta))$ = $theta w(b(theta))p_theta(theta) - lambda (b(theta)w(b(theta))p_theta(theta))$.
As Euler-Lagrange condition $fracpartial Fpartial b(theta) - fracddthetafracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)] - fracddthetafracpartial Fpartial b'(theta)=0$.
In last term $fracpartial Fpartial b'(theta)=0$.
so,
$theta p_theta(theta)fracpartial w(b(theta))partial b(theta) - lambda[w(b(theta))p_theta(theta) + b(theta)fracpartial w(b(theta))partial b(theta)]=0$
Is it correct?
calculus-of-variations lagrange-multiplier euler-lagrange-equation
asked Aug 26 at 13:53
watseob
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