This is due to the opposite signs of these terms in the augmented Lagrangian. It is also seen that, as the Lagrange multiplier λ 1 increases, the steam consumption of the crystallizer 1, W stea m 1, decreases while the expected steam consumption of the crystallizer 1, W ^ stea m 1, increases. ![]() It is noted that the primal variables as well as the Lagrange multipliers converge to the optimal values obtained by the centralized approach. Figure 3 shows the comparison of hierarchical coordination and the centralized solution for the point in time at 4,200 seconds. The Lagrange multipliers and slack variables are initialized at zero. The tuning parameters ( ρ 1, ρ 2) are set to (50, 30). The hierarchical coordination presented in section 3.3 is applied and its performance is evaluated.
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