If there are only equality constraints, GlobSol finds approximate
feasible points by generalized Newton iteration on the underdetermined
system C(X)=0, where C is as in Problem 2.
That is, iteration of the form
are used, where 
is the Moore-Penrose inverse of the
Jacobi matrix of the constraints; see [15]
for a review of the theory. GlobSol combines the iteration
13 with a special random search to generate
feasible points effectively.
If inequality constraints 
are also part of the problem,
they are ignored during the iteration if they are satisfied at the
present iterate. If, at the present iterate X, some 
,
is subsequently treated as an equality constraint 
.
For details, see [9].