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I have a linear program: minimise $f^T x$ with equality and inequality constraints.

This does not have a unique solution, so I would like to find the solution of this that also minimises $g^T x$.

One approach to doing this is to solve a second linear program with the additional constraint $f^T x = f_{min}$.

In my case, it seems that finding this second minimum takes significantly longer than finding the first.

Is there any way of expressing this process as a single linear program? Or any other better way of tackling the problem?

mikado
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  • Depending on the software you're using this could be more difficult because the feasible region is much smaller. One simple solution is to use a warm start, ie start from the original solution for the new problem. Most linear programming packages support this. – ericf Oct 15 '19 at 21:47
  • I disagree that this is a duplicate of the other question, as one is a theoretical solution for an exam and this one sounds like a practical question. – ericf Oct 23 '19 at 00:04

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