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where \(x\in\mathbb{R},y\in\mathbb{Z}\). The functions do not need to be continuous nor differentiable.
To make this simple for you, here’s a handy bestiary for thee noobs:
| Class | Convex | Nonconvex | Discrete | Pure binary | Discontinuous/non-smooth functional forms | Subclasses |
| Linear | N/A | N/A | Yes | Yes | N/A | LP, BLP, MBLP, ILP, MILP |
| Quadratic | Yes | Yes | Yes | Yes | N/A | QP, QCP, QCQP, BQP, BQCP, BQCQP, MBQP, MBQCP, MBQCQP, IQP, IQCP, IQCQP, MIQP, MIQCP, MIQCQP |
| General nonlinear | Yes | Yes | Yes | Yes | Yes | NLP, BNLP, MBNLP, INLP, MINLP, DNLP, DBNLP, DMBNLP, DINLP, DMINLP |
If you have any knowledge of the field whatsoever, you know that this is basically any problem up to and including DMINLP.
Factoring in the convex/nonconvex combinations, this gives us a whooping 55 distinct problem types that you can solve with Octeract Engine*.
The engine will automatically classify your problem, and use specialised algorithms for that problem class.
*No engineers were seriously harmed in the making of this engine
First of all because we say so, and tbh we know what we’re talking about.
If you think you can understand data, here’s some for you you heathen.
And we’re not talking vs open-source relics, we’re destroying solvers people use in production right now. We lap all the other MINLP solvers in most test sets, sometimes more than twice. Sucks to suck.
This is the clinical condition where people get so paranoid about someone beating their precious solvers that they don’t tell the user what on earth the solver is doing. Why? Because they want to keep it secret. Keep it safe.
Good ones too. We used systems design to code the solver, and since it is actively trying to inform you about everything, you can actually use your brain to manipulate the state machine using 90+ options.
A.K.A. it gets the least stuck. If you’ve ever tried to load a big-ass problem into a solver that needs to parse symbolic structures you know that preprocessing can get so hilariously stuck it never finishes at all. Well, ours is so fast that we do it at least twice. GG2EZ.
We talk the talk and we walk the walk. If any n00bz try to convince you they have better gear, we’ll crush them like a walnut – just send us the problem you need solved and get ready to buy the solver. We ain’t giving away free loot.
Octeract Engine is the first and only MINLP solver in the world that is built for distributed branch-and-bound. Those benchmarks^^ btw are on 1 and 8 cores. Here’s a glimpse of the carnage on HPC =>
Windows 10 and above
CentOS 7/Ubuntu 18 and above