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I have an optimization problem: [\begin{array}{l} \mathop {\max }\limits_{x,y} f(x,y)\\ 0 \le x \le g(y)\\ 0 \le y \le 1 \end{array}]

f is non linear in x and y.

f is increasing in x and decreasing in y. g(y) is increasing in y. Can we take x=g(y) to maximize f over x than after replacing x by g(y) in the expression of f we maximize f over y. the problem is now: [\begin{array}{l} \mathop {\max }\limits_{y} f(g(y),y)\\ 0 \le y \le 1 \end{array}]

Is that possible?

Thank you for your help.

wafa
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    Yes, that's correct. For any given $y$, the best choice of $x$ is $g(y)$. So $x$ can be eliminated from the problem. – littleO Mar 13 '17 at 09:46
  • Thank you, that makes me feel better, I already build a hole work based on this solution – wafa Mar 13 '17 at 11:20

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