Figure 5.

Contour plots of two examples separable parameter space WSSE objective functions for 4K (left) and 5K (right) compartment models. The grayscale represents WSSE values, and contour lines are drawn at regular intervals. Recall that the separable parameter space formulation for 4K-5K models has two nonlinear unknowns (υ₁, υ₂), and also that υ₂ is constrained to be less than υ₁ (hence the plots are only defined for regions υ₂ < υ₁). The objective functions are generally well behaved and do not show complex topological features. However, some complex structure exists in the lower-left corner near υ₁ = υ₂ line and near υ₂ = 0 which could slow convergence of gradient-descent type algorithms in these regions. These structures arise from “attraction” due to imaginary poles in the excluded υ₂ > υ₁ and υ₂ < 0 regions of the solution space.