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 $0 . So at my practise at the second iteration I got an p = -45, s1 = -1.45 (f.e.) ($\gamma$ may be negative too) and my Newton realization lie down. Mbe exist some another methods what I can use for my system? Thx!