The following MATLAB documentation provides details on how Simulink solves algebraic loops: https://www.mathworks.com/help/simulink/ug/algebraic-loops.html#bsn46y8-2.
Simulink utilizes trust-region or line-search methods to solve algebraic loops, which may require the Optimization Toolbox. More information on these methods can be found here:
- Trust-region: https://www.mathworks.com/help/optim/ug/unconstrained-nonlinear-optimization-algorithms.html#brnpcy5
- Line search: https://www.mathworks.com/help/optim/ug/unconstrained-nonlinear-optimization-algorithms.html#f15468
The fminunc function can be particularly useful in this context.
Hope this helps