  We present a derivative-based algorithm for nonlinearly constrained
optimization problems that is tolerant of inaccuracies in the data. The
algorithm solves a semi-smooth set of nonlinear equations that are equivalent
to the first-order optimality conditions, and it is matrix-free in the sense
that it does not require the explicit Lagrangian Hessian or Jacobian of the
constraints. The solution method is quasi-Newton, but rather than approximating
only the Hessian or constraint Jacobian, the Jacobian of the entire nonlinear
set of equations is approximated using a multisecant method. We show how
preconditioning can be incorporated into the multisecant update in order to
improve the performance of the method. For nonconvex problems, we propose a
simple modification of the secant conditions to regularize the Hessian.
Numerical experiments suggest that the algorithm is a promising alternative to
conventional gradient-based algorithms, particularly when errors are present in
the data.
