General purpose solving algorithm

This algorithm enable to determine approximately the solutions of a system of $n>0$ equations and inequalities in $m>0$ unknowns. Hence this method may be used to solve a system composed of $n_1$ equations $F_1(X)=0,\ldots,F_{n_1}=0$, $n_2$ inequalities $G_1(X) \ge 0,\ldots,G_{n_2})X) \ge 0$ and $n_3$ inequalities $H_1(X)\le 0, \ldots,H_{n_3}(X)\le 0$.