Maximization of a function I came up while studying

Asked May 06 '15 at 22:22

Active May 06 '15 at 22:54

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So in a problem I am trying to solve, after calculations I came up with the following function:

\begin{equation*} f(\overline{y},\theta)=\frac{e^{n\,min\{\overline{y},\theta)}-1}{n\theta} \end{equation*}

where $\overline{y}$ a vector of dimension $n$. Is there a way to pick $\theta$ to maximize this function ($\theta$ is a function of the vector $\overline{y})$. Min messes with the derivative so I can't come up with something. Everything is considered to be positive, including $\theta$ and the components of the vector. Thanks!

edited May 06 '15 at 22:54

asked May 06 '15 at 22:22

SpawnKilleR

What does $\min(\bar y,\theta)$ mean when $\bar y$ is a vector? – May 06 '15 at 23:02
I mean min of all components of the vector and $\theta$, i.e. mean between $n+1$ variables. – SpawnKilleR May 06 '15 at 23:03
Could you define how $\theta $ depends on $\bar{y}$? – The Pheromone Kid May 07 '15 at 10:47
It can be any function of the components of the vector – SpawnKilleR May 07 '15 at 16:41

Maximization of a function I came up while studying

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