# Minimize the infinity norm of a matrix equation

5 vues (au cours des 30 derniers jours)
Chou Tina le 23 Août 2011
Hi there,
There are three matrices M, N, and K.
M is a (4*4) matrix: M=[1 0 2 3; 2 1 3 5; 4 1 1 2; 0 3 4 3]
N is a (4*3) matrix: N=[3 0 4; 1 5 2; 7 1 3; 2 2 1]
K is a (2*4) matrix, which is a part of M: K=[1 0 2 3; 2 1 3 5]
There is also an unknown matrix V, whose size is (3*2).
My question is:
How to minimize the infinity norm of M+NVK by using Matlab?
And how to obtain the matrix V which can minimize the infinity norm of M+NVK ?
So Many thanks.
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### Réponses (1)

As per my understanding, you have three know matrices M, N and K, and an unknown matrix V. You want to minimize the infinity norm of M + NVK, and subsequently find out the matrix V that minimizes the infinity norm. It can be achieved in the following manner:
You can use the CVX library under MATLAB to solve this problem:
M = [1 0 2 3; 2 1 3 5; 4 1 1 2; 0 3 4 3];
N = [3 0 4; 1 5 2; 7 1 3; 2 2 1];
K = [1 0 2 3; 2 1 3 5];
cvx_begin
variable V(3,2);
minimize(norm(M + N*V*K,inf));
cvx_end
display(V)
Please refer to this stackoverflow question for more info on solving infinity norm minimization problems in matlab.
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