numerical problem of quadprog

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Mingyang Sun
Mingyang Sun 2021-4-13
评论： Bruno Luong 2021-4-13
Hi, I am trying to solve a badly scaled quadprog problem
H = [5e15, -1.66e15, 1.02e9, -1.23e10;
-1.66e15, 1.11e15, 1.42e6, 8.3e9;
1.02e9, 1.42e6, 2.5e6, 93;
-1.23e10, 8.32e9 , 93, 5e5 ]
f = [-4.76e7, 3.49e7, -2.19, 2.31e3]'
Aieq = [1/2, -1/3, 0, 0]
bieq = 0
when I try to use quadprog(H,-f,Aieq,bieq), MATLAB indicates problem successfully solved, but if you check inequality constraint manually, Aieq * x = a very very small positive number.
What is the best way to solve this numerical problem?
  1. set 'ConstraintTolerance' to a small number?
  2. set bieq = a very small negative number?
  3. rescale matrix H and f?
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Mingyang Sun
Mingyang Sun 2021-4-13
Thanks a lot for your replying, can I let
scal = sqrt(vecnorm(H))
and do
H_adj = H./(scal.'*scal); f_adj = f./scal.'
and
quadprog(H_adj,-f_adj,Aieq,bieq)?
Bruno Luong
Bruno Luong 2021-4-13
You have also to modify Aieq.

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