| # LP Formulation of - and -norm Regression The -norm regression problem: where , are given, can be written as the LP where stands for the -th row of . Similarly, the -norm regression problem: can be written as the LP CVX does not require the user to transform the problem into LP format. The following syntax will work for any : CVX implementation
    cvx_begin
       variable x(n,1)
       minimize( norm(A*x-y,p) )
    cvx_end
| A regression problem with random data , . The -norm tends to encourage sparsity of the residual vector: the top panel indeed shows a lot of the residual vector elements are zero. In contrast, the norm (bottom panel) encourages a lot of elements to have similar magnitude.