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From Vladimir Blagojevic <dov...@gmail.com>
Subject [math] Using optimization package for non linear equations
Date Thu, 28 Sep 2017 13:37:15 GMT
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

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