Could we achieve a more general optimizer by allowing it to have answers along the lines of "arbitrarily small"?

goose_r_s

How does min/maximization work for monotonic/asymptotic functions that would be min/maximized at infinity? Do we just take a "good enough" x?

jefftan

Even if not all objectives are bounded from below or bounded from above, is it still possible to reason about the existence of a greatest lower bound or a least upper bound? For example, for y=e^-x the greatest lower bound would be y=0 which really captures what we mean when we say "the minimum of e^-x"

Could we achieve a more general optimizer by allowing it to have answers along the lines of "arbitrarily small"?

How does min/maximization work for monotonic/asymptotic functions that would be min/maximized at infinity? Do we just take a "good enough" x?

Even if not all objectives are bounded from below or bounded from above, is it still possible to reason about the existence of a greatest lower bound or a least upper bound? For example, for y=e^-x the greatest lower bound would be y=0 which really captures what we mean when we say "the minimum of e^-x"