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 of the from

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.