A Derivation of the u-updates in DD-ADMM
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چکیده
Second, note that if we initialize λ to zero, it will always satisfy ∑ s:r∈R̄s λs(r) = 0, ∀r ∈ R. (This can be easily proved by induction by inspecting the updates in Eqs. 10 and 22.) Those conditions are simply the constraints of problem D (Eq. 7); hence, each iterate of the ADMM is guaranteed to produce a dual feasible solution. Furthermore, this property allows us to simplify the u-updates (Eq. 22) to:
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