Connect your moderator Slack workspace to receive post notifications:
Sign in with Slack

Exam 2018 Qu. 1

in exam 2018 qu. 1, I am not sure why the following two statements are always correct:

min_x' f(x', y) <= max_y' f(x, y') for all choices of x and y
max_y' min_x' f(x', y') <= min_x' max_y' f(x', y')

Can someone give an explanation or ideally point me to relevant literature? Many thanks.

Top comment

  • for the first inequality you can start from \(\max_y' f(x, y') >= f(x, y)\) for any choice of y by definition of the max. then use the definition of min which gives \(f(x, y) >= \min_x' f(x', y)\)

  • The second inequality comes from the definition of min and max, basically the max of the min is always smaller than the min of the max. You can try to say it in words it is very intuitive. Otherwise the first inequality is true for any x and y, you can chose in particular the y (resp. x) that maximizes (resp. minimizes) left (resp. right) hand side.

Thank you very much :)

Page 1 of 1

Add comment

Post as Anonymous Dont send out notification