  This paper explores a method for solving constrained optimization problems
when the derivatives of the objective function are unavailable, while the
derivatives of the constraints are known. We allow the objective and constraint
function to be nonconvex. The method constructs a quadratic model of the
objective function via interpolation and computes a step by minimizing this
model subject to the original constraints in the problem and a trust region
constraint. The step computation requires the solution of a general nonlinear
program, which is economically feasible when the constraints and their
derivatives are very inexpensive to compute compared to the objective function.
The paper includes a summary of numerical results that highlight the method's
promising potential.
