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April 6th, 2017, 01:59 AM  #1 
Newbie Joined: Apr 2017 From: Saudi Arabia Posts: 1 Thanks: 0  Optimization
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. 

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