Ipopt (Interior Point OPTimizer, pronounced eye-pea-Opt)

Ipopt (Interior Point OPTimizer, pronounced eye-pea-Opt) is a software
package for large-scale, nonlinear optimization. It is designed to find
(local) solutions of mathematical optimization problems in the form:

   min     f(x)
x in R^n

s.t.       g_L <= g(x) <= g_U
           x_L <=  x   <= x_U

where f(x): R^n --> R is the objective function, and g(x): R^n --> R^m
are the constraint functions. The vectors g_L and g_U denote the lower
and upper bounds on the constraints, and the vectors x_L and x_U are
the bounds on the variables x. The functions f(x) and g(x) can be
nonlinear and nonconvex, but should be twice continuously
differentiable. Note that equality constraints can be formulated in
the above formulation by setting the corresponding components of g_L
and g_U to the same value.