What's the solution for the following optimization problem? Is the constraint set convex?
$$\max_{x\in(0,1]}:\{-1-x\}$$
2026-04-01 22:16:08.1775081768
What's the solution for $\max_{x\in(0,1]}: \{-1-x\}$
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It has already be mentioned in the comments above that the maximum doesn't exist. Note that $$ \{-1-x : x\in (0, 1]\} = [-2, -1) $$ and this set does not have a maximum. Remember that the maximum is an upper bound that is itself a member of the set.
As also mentioned in the comment above, this set does have a supremum which is the least upper bound. You see that $-1$ is this least upper bound.