Min-max optimization
A min-max optimization (MMO) problem is a mathematical optimization problem of the following form: min x ∈ R d x max y ∈ R d y f ( x , y ) such that g ( x , y ) ≤ 0 {\displaystyle \min _{\mathbf {x} \in \mathbb {R} ^{d_{x}}}\max _{\mathbf {y} \in \mathbb {R} ^{d_{y}}}f(\mathbf {x} ,\mathbf {y} )~~~{\text{ such that }}~~~g(\mathbf {x} ,\mathbf {y} )\leq 0} , where f is a bounded function and g is a convex function. MMO problems play a central role in game theory, convex optimization and online machine learning.