. Author manuscript; available in PMC: 2017 Jun 11.

Published in final edited form as: SIAM J Sci Comput. 2016 Jan 6;38(1):A55–A83. doi: 10.1137/15M101110X

Algorithm 3.

Local optimization II.

{\tilde{γ}}_{k} = γ \forall T_{k} \in T

for all e_ij do

{\tilde{S}}_{i j} = \sum_{T_{k} \in T_{i j}} \sum_{l = 1}^{L} C_{ijkl} {\tilde{γ}}_{k l}

end for

for all e_ij do

Solve

\begin{array}{l} {min}_{{\tilde{γ}}_{k}^{new}} & \sum_{T_{k} \in T_{i j}} | T_{k} | {‖ {\tilde{γ}}_{k}^{new} - γ ‖}_{2}^{2} \\ \sum_{T_{k} \in T_{i j}} \sum_{l = 1}^{L} C_{ijkl} {\tilde{γ}}_{k l}^{new} & \geq 0, \\ \sum_{T_{k} \in T_{i j} \cap T_{m n}} \sum_{l = 1}^{L} C_{mnkl} {\tilde{γ}}_{k l}^{new} & \geq \sum_{T_{k} \in T_{i j} \cap T_{m n}} \sum_{l = 1}^{L} C_{mnkl} {\tilde{γ}}_{k l} - {\tilde{S}}_{m n} \\ \forall e_{m n} \in ℰ_{i j} \ e_{i j}, \forall T_{k} \in T_{i j} \end{array}

{\tilde{γ}}_{k} = {\tilde{γ}}_{k}^{new}, T_{k} \in T_{i j}

{\tilde{S}}_{i j} = \sum_{T_{k} \in T_{i j}} \sum_{l = 1}^{L} C_{ijkl} {\tilde{γ}}_{k l}

end for