Non differentiable optimisation problem |x|

Hey there, I am starting from scratch learning CVX at the moment. I wondered if you could show more work examples for non-differentiable optimisation problems. Here is my random example:

f = @(x) abs(x)

N = 128;
x = linspace(-1, 3, 200)’;
T = @(x) feval(chebpoly(0:N-1), x);
Tx = T(x);
variable c(N)
minimize( norm( Tx * c - fx, 2 ) );

In my codes, I want to interpolate |x| with a Chebyshev series. However, because of a lack of understanding, the accuracy of my codes is very poor. Is there any way to improve it? Any CVX notes for non-differentiable optimisation problems? Would learn better with sample codes and illustrations. Thank you in advance.

CVX can directly handle such non-differentiable functions as abs(x) and norm(x) in several different “norms”. if you want maximum accuracy, use these built-in capabilities. If for some pedagogical (?) reason you want to approximate these, you must follow CVX’s rules.

Have you read the CVX Users’ Guide? There are CVX examples at as well as in posts on this forum.