I don’t know of any implementation of DCCP in CVX, or any plans for one to be developed. Maybe you can take it upon yourself to add this - I’'m not saying it would be easy or possible, but the CVXQUAD https://github.com/hfawzi/cvxquad developers developed quite the add-on for CVX, so maybe you could too. I recommend you ask the DCCP authors about any plans for CVX.

As for how the DCCP package for CVXPY works, I will defer to the developes, and the CVX forum is not the place to find them hanging out. (Stephen Boyd hasn’t been seen (logged in) on the CVX forum subsequent to his post, linked below, in Sep 2012 - he’s not a big fan of MATLAB these days).

As for CVX, I can recommend you to Stephen Boyd’s Sep 2012 CVX Forum post How to handle nonlinear equality constraints? .for how to write a loop to handle equality constraints, specifically, how to handle an inequality constraint going the wrong way, which would be added to one going the convex way, to constitute the equality constraint. Of course your quadratic must be either convex or concave rather than indefinite for this to work.

Anyhow, I fail to see the fascination with the convex-convace procedure or Sequential Convex Programming (SCP). Sequential Quadratic Programming (SQP) in conjunction with BFGS Quasi-Newton update of the Hessian of the Lagrangian is a special case of Sequential Convex Programming. Any SQP implementation which is not safeguarded, such as by trust region or line search, is considered unreliable, even when applied to convex problems, The “Boyd” style SCP write ups I’ve seen, and what presumably gets implemented by the typical person not experienced with non-convex nonlinear optimization, is a simplistic totally unsafeguarded implementation. If you used a high quality non-convex nonlinear numerical optimizer, for instance, based on SQP, it may or may not be a SCP, but in any event will take care with implementation of safeguarding, and should be more reliable than a crude home-brew SCP. You may also have the option, at least for small enough problems, of using a (sort of ) rigorous global optimizer, such as BARON, which will accept quadratic inequalities, even for indefinite quadratics.

SCP may not converge to anything, and if it does, it is not necessarily even a local minimum of the original problem.