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[FEA] Add a way to export MPS files from C API #720

@smish-nvidia

Description

@smish-nvidia

Is your feature request related to a problem? Please describe.
I have an application that procedurally generates LPs and solves them with cuOpt. In some cases, I have observed unusual behavior or crashes when trying to solve these LPs. I would like a way to serialize the problems to disk (e.g., MPS files) so that I could share them to help the troubleshooting process.


Describe the solution you'd like
I would like to add a new function to the C API that allows a user to export a problem they've constructed to MPS format. For example:

cuopt_int_t cuOptWriteProblem(
    const char *filename,
    const cuOptOptimizationProblem *problem_ptr
)

Note: It appears as though the ability to write MPS files is already implemented in the C++ API, so it would just be a matter of exposing this capability to the C API.


Describe alternatives you've considered
I've considered using cuOpt's C++ API to export the files, but it is more challenging due to missing headers in the binary releases and the lack of stability in the API.

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