solving minimax problem with linear constraint

2016 5 30
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Hello..
I would like to solve minimax problem. This is like two-person game where x cannot depend of value of y. Variable y is bounded.
So I would ask how to solve this problem. Is it possible to solve it using fminimax since it only have one kind of objective function?
On the picture, I give a simple example of the problem I want to solve.
Best regard

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