How to effectively model "stability of a continuous variable" without causing long runtimes

Hi everyone,

I'm trying to build a model that tries to stabilize a ratio variable over time, by minimizing the absolute value of its differences between each timestep, but even with a small toy case it's spiraling into a very long solve and it's struggling to close the MIPGap.

An example below, I set up several MVars as follows:

• numerator (non-negative integer variable) with dimension: 5 types * 10 days
• ratio (non-negative continuous variable) with dimension: 5 types * 10 days
• ratio_difference (non-negative continuous variable) with dimension: 5 types * 9 days

The denominator is already known, as a constant:

• denominator (non-negative integer constant) with dimension: 5 types * 10 days

So I write the constraints as such:

• Defining the ratios: numerator == ratio * denominator
• Defining the absolute value of the ratio difference day-by-day:
  - ratio_difference >= ratio[:, 1:] - ratio[:, :-1]
  - ratio_difference >= ratio[:, :-1] - ratio[:, 1:]
• There are other constraints to the numerator, but I've omitted them here

And the objective will be minimizing the sum of ratio_difference.

With this setup, the model really struggles to close the MIP gap and produces a log like below.

Would appreciate any suggestion on how to more efficiently model such a "stability", so it's less likely to run into long runtime issues. Thanks so much in advance!