Minimize the infinity norm of a matrix equation

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.

Answer 1

[Debadipto]

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.