# Searching for numerical algorithm

I have nonlinear system of 3 equations. Here it is: $$\frac{s_2 - K_2}{ps_2^{\gamma_1} + (1 - p)s_2^{\gamma_2}} = \frac{K_1 - s_1}{ps_1^{\gamma_1} + (1 - p)s_1^{\gamma_2}} \\ \frac{s_2}{s_2 - K_2} = \frac{p\gamma_1s_2^{\gamma_1} + (1 - p)\gamma_2 s_2^{\gamma_2}}{ps_2^{\gamma_1} + (1 - p)s_2^{\gamma_2}} \\ \frac{s_1}{s_1 - K_1} = \frac{p\gamma_1s_1^{\gamma_1} + (1 - p)\gamma_2 s_1^{\gamma_2}}{ps_1^{\gamma_1} + (1 - p)s_1^{\gamma_2}}$$ Unknown variables here is $p,s_1,s_2$. At the previous topic user EMS recommend me very simple Newton Method, but here a many problems with it.

Fisrt problem what at Newton method Im need a pretty good starting point because at another way at the second iteration I may get very irreational solution (see second problem)

Second problem what there are many restrictions to my variables: $s1 \geq 0$,$s2\geq 0$ and $0<p<1$.

So at my practise at the second iteration I got an p = -45, s1 = -1.45 (f.e.) ($\gamma$ may be negative too) and my Newton realization lie down.

Mbe exist some another methods what I can use for my system?

Thx!

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maybe something like this? en.wikipedia.org/wiki/Nonlinear_programming –  Bruno Apr 10 '12 at 18:22
Pls, write it as answer and if tommorow there are no more explicit answers Il mark it as correct. –  0dd_b1t Apr 11 '12 at 8:55