The nonlinear model is similar to the linear model.

g(x) = T(Sum(i=1,d,w_i*x_i)-t) where T is some fixed nonlinear function, such as T(s)=s^2, T(s)=e^s, ...

The error function is the same as before. The optimal weights and threshold cannot be found so easily, though. The method of iterative gradient descent can be used to find local minimums. From a survey of local minimums, a global minimum can be found.