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'

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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 &#039;trick&#039;

Salma Bradley · Accepted Answer

min      x    2    ,  −  1  ≤  x  ≤  1is convex.If you consider  max      x    2    ,  −  1  ≤  x  ≤  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.

If a minimization task is a convex optimization problem, is

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