I've read optimization guide (http://commons.apache.org/pro
per/commonsmath/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
