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> their API and documentation as it's written for mathematicians and not business SMEs

I've never worked with any of these, but that's what I would expect as well. API documentation that describes how to solve each kind of mathematical optimization problem.

Do you have an example of an optimization solver with API documentation for business SMEs?

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Yeah. GUROBI makes it really easy to just do something like

m.addConstr(x+y<=limit);

Where m is a model object, x & y are decision variables and limit is a constant.

The above is a no brainer for any business expert. Some solvers are a LOT more low level though and you have to think of the problem in matrix form and specify row/column stuff and it's a lot more involved and assumes significantly more knowledge of the user than the former.

Gurobi does require you to iterate over doubly-nested arrays frequently (like when establishing a constraint between two entity sets)

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