Definition Primal and dual optimization problems [lcc-001D]

Let L: X \times Y \to \mathbb {R} be a minimax problem. The primal optimization problem associated to L is the function L^+(-) = \sup _y L(-,y): X \to \mathbb {R} (the problem being to minimize this function).

The dual optimization problem is the function L^-(-) = \inf _x L(x,-): Y \to \mathbb {R}