numerical problem of quadprog

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Mingyang Sun 2021-4-13

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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?

set 'ConstraintTolerance' to a small number?
set bieq = a very small negative number?
rescale matrix H and f?

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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 2021-4-13

You have also to modify Aieq.

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