There is a formula

\ begin {equation *}
     max_x (min _ {\ vec {y}} f (x, \ vec {y})) = sup_ {x} (INF _ {\ VEC {Y}} F (x, \ Vec {Y})) = \ gamma_1, \ Newline
     MIN _ {\ VEC {Y}} (max_x f (x, \ vec {y})) = INF _ {\ VEC {Y}} (sup_ {x} f (x, \ Vec {Y})) = \ gamma_2
\ END {Equation *}

How to postpone to a new string? \\ does not work.

Answer 1, Authority 100%

Equation is used for expressions that occupy 1 string, the multi-line multi-line expressions are used by the Multline * environment, try it.