Fig. 1

Visualisation of Cimmino’s algorithm. This figure shows the concept of Cimmino’s algorithm for a two-dimensional problem with two constraints for the iteration step \(k\rightarrow k+1\). In this case, the parameters were defined as \(w_{1,2}=0.5\) and \(\alpha =1.5\). The dashed black lines indicate the orthogonal projections of \({\mathbf {p}}^k\) onto the hyperplanes, and the dashed orange line indicates the calculation of the barycentre \({\mathbf {p}}_b^k\). A choice of different weights \(w_{1,2}\) would result in the barycentre \({\mathbf {p}}_b^k\) being shifted along the dashed orange line