Let $f(x,y)$ be a real function of the variables $x,y$ (which can be real vectors). Under what conditions do we have the following equality: $$\min_x \max_yf(x,y) = \min_y \max_x f(x,y)$$ For example, this equality is true if $f(x,y) = xy$ and $x,y$ are real scalars. Note that this is not the same as Von Neumann’s […]

# Tag: y)$ be a real function of the variables $x

Let $f(x,y)$ be a real function of the variables $x,y$ (which can be real vectors). Under what conditions do we have the following equality: $$\min_x \max_yf(x,y) = \min_y \max_x f(x,y)$$ For example, this equality is true if $f(x,y) = xy$ and $x,y$ are real scalars. Note that this is not the same as Von Neumann’s […]

Let $f(x,y)$ be a real function of the variables $x,y$ (which can be real vectors). Under what conditions do we have the following equality: $$\min_x \max_yf(x,y) = \min_y \max_x f(x,y)$$ For example, this equality is true if $f(x,y) = xy$ and $x,y$ are real scalars. Note that this is not the same as Von Neumann’s […]