given a system of inequalities expressed in the following way: A x &gt; <munder>

garcialdaria2zky1 2022-05-13 Answered
given a system of inequalities expressed in the following way:
A x > k _
where A M n , m ( R ) , with n>m, and k _ = ( k , k , , k ) R n
In general, the system might or might not admit solutions. I would like to find a solution x R m that minimizes the number of violated inequalities.
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Answers (2)

garcialdariamcy4q
Answered 2022-05-14 Author has 15 answers
A x > k is a difficult concept in optimization. Usually we deal with A x k. (If needed you can add a small number ε > 0 to k; note also that solvers typically employ a feasibility tolerance, so ε should be larger than that).
So, assume we have A x k. Next we can do
min i δ i j a i , j x j k δ i M δ i { 0 , 1 }
Here M is a large enough number.
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llunallenaipg5r
Answered 2022-05-15 Author has 5 answers
Thanks a lot for your answer, it is very very helpful!
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