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Which seems almost ironic, because continuous linear optimization almost certainly doesn't exist really because real numbers can only be approximated, and so we
by naasking 2y ago
Which seems almost ironic, because continuous linear optimization almost certainly doesn't exist really because real numbers can only be approximated, and so we're always doing discrete linear optimization at some level.
- eru 2y agoWho cares about real numbers in this context? If all the numbers that appear in your constraints are rational (p/q with finite p and q), then any solution is also a rational number (with finite nominator and finite denominator). (Well, any finite solution. Your solution could also be unbounded, then you might have infinities in there.) A computer can represent finite rational numbers just fine. See eg https://docs.python.org/3/library/fractions.html https://docs.python.org/3/library/fractions.html or https://hackage.haskell.org/package/base-4.20.0.1/docs/Data-Ratio.html https://hackage.haskell.org/package/base-4.20.0.1/docs/Data-... for some libraries. Though in most cases, people just use floating point numbers in practice, but that's of no philosophical concern.