Figure 4.

Objective function as a function of executed integrations. Using only central finite differences (cfd), resembling the search directions of a quasi-Newton solver or cfd together with shape constraints (shape) leads to a slow decrease in the residual sum of squares. The use of null-space-based sampling (null) significantly increases the convergence speed. Combining the null-space-based sampling with shape constraints leads to a slight improvement. Even better results are obtained when thresholds for improvement within the current stencil are introduced. Using a threshold of minimally 1% improvement in objective function (acc) to keep the stencil reduces inefficient iterations (green line).