Maximization problem
= Maximization problem
{title2=$\sup_{u\in F}f(u)$}
A maximization problem seeks a feasible point with largest objective value. Its supremum can fail to be attained or be infinite. Negating the objective gives a <minimization problem>. A global extremum of an <optimization Lagrangian> can certify a feasible optimum by the <Lagrangian sufficiency theorem>.