What file formats does your solver support?

Octeract Engine supports .mod, .nl, .gms, .mps, .lp, and .py (Pyomo) file formats.

What is Deterministic Global Optimisation?

Deterministic global optimisation (DGO) is the science of solving a non-convex optimisation problem while, at the same time, obtaining a certificate of global optimality for the result.

In other words, it is the branch of optimisation which studies how to guarantee global optimality for non-convex problems. This also implies that DGO is the only way to prove/disprove infeasibility of a non-convex problem.

How big are the problems you can solve?

It highly depends on the math involved, and the domain of definition.

The largest MINLP we have solved during our testing had about 110,000 continuous variables, 100,000 constraints, and 14 binaries. The largest NLP was about 200,000 x 200,000

Due to the fact that we could exploit special structure, this was solved to global optimality in about 40 seconds. In contrast, small problems of about 10 variables can take minutes or even a few hours if the functions are highly non-linear and full of singularities.

Do I need a powerful machine?

Octeract Engine is lightweight and memory friendly and will run on any modern computer. Very large problems inevitably take up much more memory and power to solve; therefore we recommend at least 4 physical cores and 8GB of RAM if you are running large problems in parallel mode, and as much virtual memory as you can spare.

In most cases we are able to detect and exploit special structure, which can improve performance tremendously, thus reducing the computing requirements for the user.

As a rule of thumb, the main factors which contribute to CPU time cost are:

• the number of variables and constraints
• the degree and type of non-linearity in your problem expressions
• the level of sparsity of the Hessian and the Jacobian of your problem
Is there a cloud service?

Not at the moment, but if this is a feature you need, you are most welcome to submit a

Are there performance benchmarks?

As always, the best way to gauge a solver’s performance for your particular problems is to try it out yourself. If you are feeling a wee bit lazy, Octeract Engine has been benchmarked by Prof. Hans Mittlemann.

The solver is stable across a test set of 3,016 problems of varying size, sparsity, and nonlinear structure, and solves half of these problems in under a minute using only one CPU.

Our internal benchmarks and statistics can be found on our benchmarks page.

How rigorous is the guarantee of optimality?

Octeract Engine has implementations of algorithms that guarantee convergence to a global optimum in finite time. The methods are discussed across thousands of publications on Deterministic Global Optimisation, such as this one.

The correctness of the majority of numerical calculations is ensured through a combination of interval arithmetic and infinite precision arithmetic. Of course, this guarantee can still be compromised due to undiscovered bugs in the software and/or floating-point errors from third-party dependencies.

If your question hasn’t been answered, you’re welcome to get in touch to let us know what’s on your mind. We’ll answer your questions as soon as possible.

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