The translation from continuous to discrete is not automatic. There is a missing verification in the linked analysis. The mapping must be verified for stability for the proper class of initial/boundary conditions. Increasing the resolution from 64 bit floats to 128 bit floats doesn't automatically give you a stable discretized optimizer from a continuous formulation.

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phyalow 14 hours ago | parent [-]

Or you can just try stuff and see if it works

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measurablefunc 14 hours ago | parent [-]

Point still stands, translation from continuous to discrete is not as simple as people think.

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phreeza 13 hours ago | parent [-]

Numerical issues totally exist but the reason has nothing to do with the fact that Cauchy sequences don't exist on a computer imo.

	▲	measurablefunc 7 hours ago \| parent [-]
		The abstract formulation is different from the concrete implementation. It is precisely b/c the abstractions do not exist on computers that the abstract analysis does not automatically transfer the necessary analytical properties to the digital implementation. Cauchy sequences & Dedekind cuts are abstract & do not exist on digital computers.