Hi
I am trying to solve the following problem :
(1) max_{x in X} min_{y in Y} f(x,y)
I need to convert (1) to a minimax problem for some algorithm, i.e. of type
min max g(x,y), where g(x,y) contains f(x,y). Here is my solution :
A. If we start from the outer layer in (1), since min h = -max -h, we
get
-min_{x in X} - min_{y in Y} f(x,y)
B. We now convert the inner problem to a max problem, so we get
(2) -min_{x in X} max_{y in Y} -f(x,y)
Is (2) the minimax problem of the maximin problem (1) ? i.e. do they
have the same optimal solution and optimal objective function value ?
-frege
I am trying to solve the following problem :
(1) max_{x in X} min_{y in Y} f(x,y)
I need to convert (1) to a minimax problem for some algorithm, i.e. of type
min max g(x,y), where g(x,y) contains f(x,y). Here is my solution :
A. If we start from the outer layer in (1), since min h = -max -h, we
get
-min_{x in X} - min_{y in Y} f(x,y)
B. We now convert the inner problem to a max problem, so we get
(2) -min_{x in X} max_{y in Y} -f(x,y)
Is (2) the minimax problem of the maximin problem (1) ? i.e. do they
have the same optimal solution and optimal objective function value ?
-frege