Is consensus ADMM performance affected by how the objective function/ constraints are split?How to minimise...
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Is consensus ADMM performance affected by how the objective function/ constraints are split?
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I just wanted to know whether Consensus ADMM convergence results are affected by the way we split the objective function. For example, will the results be affected if I split f=f1+f2+f3+f4 as (f1+f2) & (f3+f4) or (f1) & (f2+f3+f4) ?
convergence optimization convex-optimization
asked Mar 19 at 5:09
BunaBuna
403
$endgroup$
add a comment |
$begingroup$
I just wanted to know whether Consensus ADMM convergence results are affected by the way we split the objective function. For example, will the results be affected if I split f=f1+f2+f3+f4 as (f1+f2) & (f3+f4) or (f1) & (f2+f3+f4) ?
convergence optimization convex-optimization
asked Mar 19 at 5:09
BunaBuna
403
$endgroup$
$begingroup$
In consensus ADMM the problem of minimizing $sum_i f_i(x)$ is reformulated as minimizing $sum_i f_i(x_i)$ subject to the constraint that $x_1=x_2=cdots=x_n$. The splittings you're describing don't sound like the consensus trick to me. But yes, I think the choice of how you split $f$ could affect the number of iterations required for convergence.
$endgroup$
– littleO
Mar 19 at 5:51
add a comment |
$begingroup$
I just wanted to know whether Consensus ADMM convergence results are affected by the way we split the objective function. For example, will the results be affected if I split f=f1+f2+f3+f4 as (f1+f2) & (f3+f4) or (f1) & (f2+f3+f4) ?
convergence optimization convex-optimization
asked Mar 19 at 5:09
BunaBuna
403
$endgroup$
I just wanted to know whether Consensus ADMM convergence results are affected by the way we split the objective function. For example, will the results be affected if I split f=f1+f2+f3+f4 as (f1+f2) & (f3+f4) or (f1) & (f2+f3+f4) ?
convergence optimization convex-optimization
convergence optimization convex-optimization
asked Mar 19 at 5:09
BunaBuna
403
asked Mar 19 at 5:09
BunaBuna
403
asked Mar 19 at 5:09
BunaBuna
403
asked Mar 19 at 5:09
BunaBuna
403
asked Mar 19 at 5:09
BunaBuna
403
403
$begingroup$
In consensus ADMM the problem of minimizing $sum_i f_i(x)$ is reformulated as minimizing $sum_i f_i(x_i)$ subject to the constraint that $x_1=x_2=cdots=x_n$. The splittings you're describing don't sound like the consensus trick to me. But yes, I think the choice of how you split $f$ could affect the number of iterations required for convergence.
$endgroup$
– littleO
Mar 19 at 5:51
add a comment |
$begingroup$
In consensus ADMM the problem of minimizing $sum_i f_i(x)$ is reformulated as minimizing $sum_i f_i(x_i)$ subject to the constraint that $x_1=x_2=cdots=x_n$. The splittings you're describing don't sound like the consensus trick to me. But yes, I think the choice of how you split $f$ could affect the number of iterations required for convergence.
$endgroup$
– littleO
Mar 19 at 5:51
$begingroup$
In consensus ADMM the problem of minimizing $sum_i f_i(x)$ is reformulated as minimizing $sum_i f_i(x_i)$ subject to the constraint that $x_1=x_2=cdots=x_n$. The splittings you're describing don't sound like the consensus trick to me. But yes, I think the choice of how you split $f$ could affect the number of iterations required for convergence.
$endgroup$
– littleO
Mar 19 at 5:51
$begingroup$
In consensus ADMM the problem of minimizing $sum_i f_i(x)$ is reformulated as minimizing $sum_i f_i(x_i)$ subject to the constraint that $x_1=x_2=cdots=x_n$. The splittings you're describing don't sound like the consensus trick to me. But yes, I think the choice of how you split $f$ could affect the number of iterations required for convergence.
$endgroup$
– littleO
Mar 19 at 5:51
add a comment |
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$begingroup$
In consensus ADMM the problem of minimizing $sum_i f_i(x)$ is reformulated as minimizing $sum_i f_i(x_i)$ subject to the constraint that $x_1=x_2=cdots=x_n$. The splittings you're describing don't sound like the consensus trick to me. But yes, I think the choice of how you split $f$ could affect the number of iterations required for convergence.
$endgroup$
– littleO
Mar 19 at 5:51