ITERATION_LIMIT with small changes in constraints

Specific Domains Optimization (Mathematical)
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1

I have a linear problem with linear equality and inequality constraints (and interval constraints). It works perfectly with various lower and upper bounds, but specific values trigger this ITERATION_LIMIT and there is nothing special about these values.

For example, the upper bound 34000 works fine but 34060 doesn’t. I understand that this may be related to numerical issues with the underlying solver, would this be a correct interpretation of the issue? Increasing the upper bound would make the problem “more feasible” and yet I get this unexpected return status.

I am using the COSMO.jl solver in this application, it works pretty well and is pure Julia :heart: By default I am setting the relative tolerance to eps_rel=1e-8. Whenever I get ITERATION_LIMIT I increase the tolerance to 1e-4 and it solves the problem again, but I am not sure if the result is accurate enough.

2

It’s hard to say anything without a reproducible example. What do other solvers do? Try HiGHS or Gurobi.

3

I tested with HiGHS.jl and it doesn’t display this problem @odow , so the issue must be specific to COSMO.jl.

4

If just have a linear program, then just use HiGHS, it should be faster and more robust.

You don’t gain anything by using COSMO, which is more intended for conic problems. And I assume the numerics of your problem are bad, which is why COSMO struggles.

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