IMPORTANT what should be my first guess?

Im planning to solve the following problem with trial and error in c++

 

find the minimum value of the following function .

 

 

 

"yi" and "xi" are the result of a complicated analysis on my lab data and I need to find a,b,c in a way that COST(a,b,c) function to be minimum.

 

after solving this equation by calculating the partial derivatives and force them to be equal to ZERO we obtain the attached equations for a b c.

as you can see we have to use the trial and error method to solve this problem for a b c

the problem is the first guess of a b c. based on the first guess the answer changes and usually goes to infinity !!!

Im asking you to help me to find the proper first guess.

Ive attached a set of sample xi yi data to the post too. data_file.txt

just in case I attach the c++ class I have programmed to this post too. PowerRegression.zip

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