How to express L0 norm of a vector of norms?

MIDCP
#1

I have a variable defined as A(100\times 5) which is complex

      variable A(100,5) complex

Then I define as expression as

      expressions B(5,1) nonegative

      B=[norm(A(:,1)) norm(A(:,2)) norm(A(:,3)) norm(A(:,4)) norm(A(:,5))];

Now my objective is to minimize the L0 norm of vector B, i.e., minimize the number of non-zero elements in vector B

\min ||B||_0

Can it be done in CVX?

#2

Paul Rubin’s answer can be implemented in CVX.

1 Like
#3

Let,

C=5;
U=10;
N=4;
bigM=1000;

I have done the following

  variable Z(C,1) binary
  variable A(N*C,U) complex
  expressions b(C,1) nonegative


   cvx_begin
   for c=1:C
      b(c)=norm(vec(A((c-1)*N+1:c*N,:)));
   end

   minimize sum(Z)

   subject to

   for indx=1:C
       b(indx) >= 0;
       b(indx) <= bigM*Z(indx);
   end

is nor working as we have DCP error!

#4

This

b(indx) >= 0;

is not needed and even cannot be used. A norm is always nonnegative.

Isn’t the whole loop just

b <= bigM*Z

?

#5

This I tried and I do not get any error.