binary quadratic optimization under linear constraints

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alessio morabito 2021-3-20

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评论： alessio morabito 2021-3-28

Hi guys.

I have to find an optimal gradient and intercept of a straight to minimize the sum of squared deviations to fit a 2D data points set, with linear constraints.

So, i have to solve the binary quadratic optimization problem: minF(ki,bi)=min(sum(ki*xj+bi-yj))^2 where (xj,yj) are the coordinates of the j-th data set point.

i have also to define some constraints, such as:

ki<=Kmax;

Hmin <= ki*xj+bi-yj <= Hmax

i've tried to use fmincon and quadprog but i was not able to solve my problem. could someone give me some tips?

many thanks

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Answer 1

John D'Errico 2021-3-20

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How is this not just a linear least squares estimation of the two unknown parameters? There is nothing binary about this, except that you have two unknowns. That is a misuse of the word, and will just confuse people.

As far as the quadratic optimization goes, again, you are trying define the problem in terms of flowery words, when a simple solution exists.

While you can use polyfit but for the constraints, those constraints make it a problem for lsqlin, which can trivially solve your problem. This is a simple linear least squares estimation problem, subject to linear inequality constaints.