Generally a quadratic model, a polynomial of degree two will be good.
Response surface methodology with CCD (Central composite design) may lead you towards quadratic model
LINGO is best because price is cheap and there are many functions and easy usage and many samples. See my papers by LINGO.
You can go for LINGO software of Lindo system as said above. Also, you can use optimization toolbox of MATLAB or similar package in R. Since R is free, so it would be easy. If the optimization problem is simple, you can even solve it in MSExcel using the powerful excel solver.
See two files.
I believe the best software improves our producivity of researches.
I published many papers by many data and am successful in the discrimination of microarray data because I use powerful LINGO..
It depends upon how we have command on any tool. ARENA a simulation software gives a best fit non-linear model with minimum error and follow closely the trend of data
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