# How to minimize this non-linear function?

minimize the following function:

$$\sum^n_{v=1}\left(S_{1v} - t \frac{(1-p_v)\sin r_v }{1-p_v\cos r_v }\right)^2 + \left(S_{2v} - t \frac{(1-p_v)\sin (6r_v) }{1-p_v\cos (6r_v) }\right)^2$$

subject to inequality constraints:

$$\begin{bmatrix}-t \\ p_v -1 \\ -p_v \\ r_v - \pi/12 \\ -r_v\end{bmatrix} \le 0$$

where $S_1, S_2, p, r$ are vectors with $n$ elements, $t$ is a scalar, and $v=1,..., n$

$S_1$ and $S_2$ are the observations. $t$, $r$ and $p$ are the unknowns. I have very good initial values for $r$ and $p$. My question is: how to estimate $t$, $r$ and $p$?

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You are minimizing over unknown real scalar $t$ and functions $p, r$? In what function space? –  user7530 Sep 13 '13 at 13:13