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There is a least-squares problem. It can be solved using backslash in Matlab.
If Ax = b, then x = A \ b.
Let's assume that I have the same problem, but all x must be non-negative (>=0). How can I solve this problem in Matlab by analogy with the previous one (without non-negativity constraints)? I think it can be somehow connected with the active set method.
I know that the non-negative least squares problem can be easily solved with Matlab Optimization toolbox or CVX or in many other ways. But still I'm curious about solving it by analogy with a straight-forward least-squares method (with backslash).
Could anyone help me please?

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MATLAB has a built-in function lsqnonneg() which is an implementation of the active set method described in the book "Solving Least Squares Problems" by Lawson and Hanson (1974)

The \ solution of linear least squares problems in MATLAB is done by a variety of different algorithms depending on the exact structure of the problem. None of them are particularly similar to the active set method used in lsqnonneg().

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Not sure if this helps, but the trick is that Lawson & Hanson's algorithm selects a special subset of columns from A such that when you perform regression x = A(:,subset) \ b resulting coefficients are all non-negative.

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