I've read optimization guide (http://commons.apache.org/pro per/commons-math/userguide/optimization.html) yet I'm still unsure about how to apply optimization examples in my case.
I have a set of nonlinear equations in the form: e^(qt)S - e^(rt)K1 = b1 e^(qt)S - e^(rt)K2 = b2 ... e^(qt)S - e^(rt)Kn = bn r and q are unknown variables (parameters?), while S, t, K1...Kn are known scalars. b1...bn is a set of known scalar observations that could contain errors. Since r,q are two unknown variables I could simply solve the set of two equations b1,b2 and find the desired q and r. However, those two particular observations b1 and b2 could contain the most error in observation set data thus propagating the error to r and q. How could I use optimization package to find optimal r and q for the entire set of observations that would minimize the sum of the difference? Regards, Vladimir
