Hi, I’m new with cvx. I know that this problem is not convex but is there any way of solving the optimization problem minimize( norm(A*x-b, 1) ) subject to norm(x,2)==1?

I wrote this code:

clear;

close all;

clc;

n = 8;

d = 3;

A = randn(n,d);

b = randn(n,1);

cvx_begin

variable x(d)

minimize( norm(A*x-b, 1) )

subject to

x’*x <= 1;

cvx_end

fprintf(‘norm(x) = %f\n’,norm(x));

If I change x’*x<=1 to x’*x==1 it won’t work, but even for this code it sometimes prints that norm(x) is exactly 1. Meaning, cvx actually do solve my problem sometimes. but I need it to always solve it. is it possible? (in Yalmip it worked so I know the problem is solvable).

Thanks