If a minimization task is a convex optimization problem, is the maximization of the same objective function also always a convex optimization problem?
My guess is yes since minimization of the negative of the objective function is maximization, but wondering if there are cases that outdo, and disprove, this sign 'trick'
$$\min x^2,$$$$ -1 \le x \le 1$$ is convex.
If you consider $$\max x^2 ,$$$$ -1 \le x\le 1,$$
It is clearly not convex, in particular, it attains the maximum at the boundary but if we interpolate it, we do not get an optimal solution in between.