Dcp Requirement Violated When Specifying Constraing In Cvxpy, Perhaps Need To Rethink Entire Formulation Of Problem

This is a follow-up to an earlier specific question, but as I add more complexity to the problem formulation, I realize that I need to take a step back and consider whether cvxpy

Solution 1:

Just transform it:

constr8 = (tot_util/cp.sum(dec_vars)) >= 1.3

->

constr8 = tot_util >= 1.3 * cp.sum(dec_vars)

You might need to enforce that cp.sum(dec_vars) is positive though or else: 0 >= 0 is a valid solution.

See also: lpsolve docs: Ratios

Side-remark

Yes, you are targeting machine-learning scale data with general-purpose optimization tools which will quickly hit a limit, even for pure continuous cases. In your case, using discrete-optimization, you probably will run into scalability issues (sounds like 1M binary-variables), especially when limited to open-source solvers.