. Author manuscript; available in PMC: 2018 May 1.

Published in final edited form as: IEEE Trans Ultrason Ferroelectr Freq Control. 2017 Mar 14;64(5):811–825. doi: 10.1109/TUFFC.2017.2682061

Algorithm 1.

Stochastic gradient descent (SGD)

Input: c₀, λ

Output:

\hat{c}

k ← 0 {k is the algorithm iteration number.}

while stopping criterion is not satisfied do

Draw w_k according to chosen distribution.

Calculate

G_{k} \leftarrow \nabla_{c} f (c_{k}, w_{k}) + λ \nabla_{c} ℛ (c_{k})

Choose step size α_k

c_k₊₁ ← c_k−α_kG_k

k ← k+1

end while

\hat{c} \leftarrow c_{k}