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April 6th, 2017, 01:59 AM   #1
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Joined: Apr 2017
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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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