Hi all.(adsbygoogle = window.adsbygoogle || []).push({});

I was thinking on how we can maximize a function with the following form:

F(y, x_{1}, x_{2},..., x_{n}) with y=f(x_{1})

I know that I should use the total derivative to find out the effective rate of y, but I don't see how gradient and Hessian should be organized in this context.

For example, if we have F(y, x_{1}, x_{2}) with y=f(x_{1}), how should we set gradient and Hessian?

Should the gradient be [itex]\nabla[/itex]F= (F_{1}, F_{2})?

Or [itex]\nabla[/itex]F= (F_{y}, F_{1}, F_{2})

What about the Hessian?

Sorry for the question (maybe not exactly challenging...), but this problem is not explicitly mentioned in any book.

Thanks.

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# How to maximize when two variables depend on each others

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