Dear Sir,
I have developed regression models and used solver to find the constants. This worked well, however, in my case I found I was able to achieve a much greater R2 using a multilayer perceptron as a universal function estimator and solving the weights. I found that solver would get stuck in local maxima and minima quite easily, so i ended up using evolutionary techniques to solve the weights. The original model was sinusoidal with 10 constants, and using solver i achieved an R2 of around 0.6. With the MLP and evolutionary techniques, I was able to achieve an R2 of 0.95.
I wish you the best in your endeavours.
Kind regards,
Nick Emblow