I am working on a regression problem with L1-norm regulation. My objective function is in this form, maximize(-0.5*(Y-D(MW)+)-0.1*sum(abs(W)) ), given D and M, optimize W. And (MW)+ means max(MW, 0).
The dimension of Y is n-by1, D is n-by-m, M is m-by-m, and W is m-by-1;
When I wrote my objective function in this cvx in this form:
cvx_begin quiet
variable w(mLen, 1)
variable w0
maximize( -0.5* norm(Y-fitD*max(fitM*w, 0)- w0)- 0.1*sum(abs(w)) )
subject to
w >= 0;
w0 >= 0
cvx_end
I got the error:Cannot perform the operation norm( {concave}, 2 ).
I would like to ask if there is a way to write this objective so CVX ruleset accepts.
Thank you, and any help would be appreciated!