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Answer was for previous version of problem
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Edit: the answer below ignores the monotonicity constraint, and refers to a previous version of the problem with $g(h(n))$ instead of $h(g(n))$

You problem is completely separable: for each $k$, choose the value of $h(k)$ such that $g(h(k))$ is as close as possible to $f(k)$, a decision that is independent from the values of $h(n)$ for all other $n \neq k$. Each of these choices is made by simple inspection of the possible values for $g$.

You problem is completely separable: for each $k$, choose the value of $h(k)$ such that $g(h(k))$ is as close as possible to $f(k)$, a decision that is independent from the values of $h(n)$ for all other $n \neq k$. Each of these choices is made by simple inspection of the possible values for $g$.

Edit: the answer below ignores the monotonicity constraint, and refers to a previous version of the problem with $g(h(n))$ instead of $h(g(n))$

You problem is completely separable: for each $k$, choose the value of $h(k)$ such that $g(h(k))$ is as close as possible to $f(k)$, a decision that is independent from the values of $h(n)$ for all other $n \neq k$. Each of these choices is made by simple inspection of the possible values for $g$.

Source Link
F_G
F_G
  • 837
  • 5
  • 7

You problem is completely separable: for each $k$, choose the value of $h(k)$ such that $g(h(k))$ is as close as possible to $f(k)$, a decision that is independent from the values of $h(n)$ for all other $n \neq k$. Each of these choices is made by simple inspection of the possible values for $g$.