Constained regression 2 - regression model/solver

I have a regression model log (r(i)) = a + b * log(A(i)) where A(i) is a vector and each element is known. Log is the nature log.

I need to find out a, b, and each element of r(i) such that the sum of r(i) equals to a constant k and the sum of error, sum(square[log (r(i)) – log(P(i)])is minimized, here each element in vector P(i) is known. a and b are scalars.

What regression model/solver should I choose? How to accomplish this gooal?

Thanks!

[dpb]

How do A and P relate to each other?

[John D'Errico]

A virtually identical re-ask of your last question, except that in this version, the main difference is you added the Thanks! at the end.

http://www.mathworks.com/matlabcentral/answers/182905-what-constrained-regression-function-shuld-i-use

Answer 1

[Torsten]

min: sum_{i=1}^{N} (log((a+b*log(A(i))/P(i)))^2

under the constraint

exp(a)*sum_{i=1}^{N} A(i)^b - k = 0

Use fmincon to solve for a and b.

Best wishes

Torsten.