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.