How to solve linear system of equations which have inequality constraints? y = m i

Cory Patrick

Cory Patrick

Answered question

2022-06-16

How to solve linear system of equations which have inequality constraints?
y = m i n x 1 2 | | D x d | | 2 2
s . t .
A x c

Answer & Explanation

pyphekam

pyphekam

Beginner2022-06-17Added 27 answers

It will strongly depend on how the problem is posed. Say, if A x c is a compact region R, you can apply Weierstrass Theorem and optimize inside it with the Differential of y and then comparing with the values of the border of the region, as usual. Of course this could mean a lot of work, depending on R. If R is not a compact region I would try to check the growth of y along unbounded direction to get a glimpse of what's going on.
If y were linear you have the simplest case since the optimization point lies in a vertex (or segment joining two vertices), but unfortunately this is not your case, as you probably already know according to your remark.

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