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Step 3: Based on the observed outage probability, the primary link would update the respective λ based on the dual update scheme and calculate the approximate gradient.
Nevertheless, in [14] we elaborate an efficient numerical algorithm based on the dual update methods [19, 20] which defines a polynomial complexity algorithm along with a reduction of the number of variables to be optimized.
The secondary user updates power levels as primal update scheme while primary links would observe the outage events and feedback the respective information through λ as dual update scheme.
Based on the iterative scheme of strictly contractive semiproximal Peaceman-Rachford splitting method, our proposed FSR-SADMM can significantly reduce the total iteration count while only involving additional dual update (i.e., (lambda^{k+frac {1}{2}})) which added negligible computational burden for each iteration.
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The result is a primal-dual update scheme in a stochastic setting.
Given a close deterministic approximations of gradient Θ k (n), the above SDLA-I can be treated as a deterministic primal-dual update algorithms.
Intuitively, this dual variable update approach can be interpreted as follows.
The purpose of the primal iteration (S1) is to compute the stochastic subgradients in (S2) that are needed to implement the dual descent update in (S3).
On the other hand, if user k has a lower data rate than R t, the dual variable update allows it to increase its λ k and so its powers' value, it can then reach R t by earning more RB or by raising its consumed power amount.
The local variable and dual variable updates are carried out independently in parallel by all BSs, while the global variable update is carried out by BS coordination.
Discarding the values that result from P ̂ i k = 0, we obtain the reduced list { λ ̆ i k } and finally, the dual projection updates μ k from { λ ̆ i k } by doing μ k + 1 = min { λ ̆ i k } (46).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com