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May 19th, 2015, 02:07 PM   #1
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Derivative vector of a function

Hi guys!

I would like to maximize the following function with respect to $\displaystyle w_t$ (which is a 1x4 vector of weights).

$e(w_t) = m_{1pt+1}(w_t) - 1/2 * m_{2pt+1}(w_t) + 1/6 * m_{3pt+1}(w_t)$

s.t

$m_{1pt+1}(w_t)=w'_t\mu_i$

$m_{2pt+1}(w_t)=w_tM_{2,t+1}w'_t$

$m_{3pt+1}(w_t)=w'_tM_{3,t+1}(w_t \otimes w_t)$

where $\mu$ is a 1x4 vector of means, and $M_2$ and $M_3$ are 4x4 and 4x16 moment matrices respectively.

In order to maximize the function I need a derivative vector (I'm going to program it in a statistical software). Could you please tell me what will be the dimensions of the derivative vector and tell me how to calculate it? The main difficulty is that the derivative is supposed to be with respect to $w_{it}$, where i ={1,2,3,4).

Any help would be greatly appreciated.
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