How does the simplex algorithm apply to the non-linear Hill model in Di Veroli 2015? In Di Veroli 2015 they claim to use simplex-based algorithms, including standard simplex, to a multivariable Hill model
$$E(C; E_{\infty,i}, \cdots, E_{\infty,n}, \text{EC}_{50_1}, \cdots, \text{EC}_{50_n}, H_i, \cdots, H_n) = \prod_i^n \left(1 + \frac{E_{\infty,i} - 1}{1 + \left( \frac{\text{EC}_{50_i}}{C}\right)^{H_i}} \right)$$
I thought standard simplex was for linear systems, but I don't see a linear combination here even after a log transform. How is this achieved?

I think they must mean the Nelder-Mead simplex algorithm, which has nothing to do with linear programming. It's a derivative-free hill-climbing method that involves heuristic strategies for improving a simplex of 'working' points
