I would be grateful for suggestions to solve the following problem.
The task is to fit a mechanistically-motivated nonlinear mathematical model (4-6 parameters, depending on version of assumptions used in the model) to a relatively small and noisy data set (35 observations, some likely to be outliers) with a continuous numerical response variable. The model formula contains integrals that cannot be solved analytically, only numerically. My questions are:
1. What optimization algorithms (probably with stochasticity) would be useful in this case to estimate the parameters?
2. Are there reasonable options for the function to be optimized except sum of squared errors?