lsquares fitting and constrains for parameters (looking for positive values of parameters)

>> > If you do not need a symbolic solution,
>>
>> You're right. I need concrete values. (I've forgot to say it in
>> problem statement).
>>
>> > you might be interested in
>> > fmin_cobyla, which will produce the minimum of a function subject to
>> > equality or inequality constraints.
>>
>> fmin_cobyla, I haven't knew about it. (btw. I see it's implemented in
>> Scipy as well.)
>>
>> I try to figure out how to make it to obey constraints, with no
>> success. Results are not positive, and even worse than
>> lsquares_estimate.
>>
>> As I doing sth wrong ?
>> Or sum equations are not fmin_cobyla's purpose, are they ?
>>
>
> From what I can see, you're doing everything correctly.? I have noticed that
> fmin_cobyla is sensitive to the initial guess.?? With your example,
> fmin_cobyla does return positive values for the parameters, except a3, which
> is very small and slightly negative.
>
> It's also possible that by giving a too-complicated expression makes cobyla
> less efficient.? Just from looking at the data matrix, it's clear that the
> relationship is linear (difference each y value is a constant).
>
> Perhaps a better example would be a real cubic with some noise added to the
> y values.
>
> Ray

Thanks for ensuring me I am doing everything fine.

Now I know, it's question of "workarounds" and "tuning" to make all
this stuff work as expected :).

All Best,
Greg