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I'm using cvxpy to model a problem. Inside a very large and complex LP, I create two continuous, affine (unconstrained) expressions: $x$ and $y$. Due to how they are created, I know that $0\lt x \lt y \leq U$. Obviously: $x/y \lt 1$.

In my LP objective, how do I maximize the ratio $x/y$?

Things I tried:

  • Maximizing x*cp.invpos(y) states my problem is non DCP (also if I try to minimize the inverse)
  • I found various LP formulations for maximizing ratios (e.g. here or here) but these requires rewriting the constraints on all the terms in the expressions for $x$ - I have no idea how to do that with cvxpy.
    If this is the way to go then an example would be very helpful!
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  • $\begingroup$ @Mason the measure I need to maximize needs to be a “unitless” proportion between 0-1 so that it it properly scaled with other measures in the objective. $\endgroup$ – Adi Shavit Oct 15 at 18:05
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CVXPY makes this easy to do, using its disciplined quasiconvex programming (DQCP) capability.

An example is provided at https://www.cvxpy.org/examples/dqcp/concave_fractional_function.html . Fractional Linear programming, as you have, is a simple special case of this.

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