#askmath — Public Fediverse posts

OK I'm going to need ask the Fediverse for some math help here, because I have a feeling I'm forgetting something obvious and can't find the resources I'd need to answer my own question.

Let's say I have an underdetermined linear system. The methods generally employed to solve these find the least (l2) norm solution, which is generally acceptable.

However, in my case, I need to find solutions that satisfy some constraint (simple inequality constraints: solution must be in a box, with known ranges [min max] for each variable).

I think I have had a brain freeze because the only approach I can think of to solve this is to turn the problem into a constrained optimization problem. However, in my case (hundreds of thousands of variables) this is not computationally feasible: the time needed for the optimization approach is ridiculously higher than the standard linear system solution.

OTOH, I have a vague feeling that it should be possible to approach this differently, possibly remaining in the domain of the linear system resolution. What am I missing?

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