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We present a derivative-based algorithm for nonlinearly constrainedoptimization problems that is tolerant of inaccuracies in the data. Thealgorithm solves a semi-smooth set of nonlinear equations that are equivalentto the first-order optimality conditions, and it is matrix-free in the sensethat it does not require the explicit Lagrangian Hessian or Jacobian of theconstraints. The solution method is quasi-Newton, but rather than approximatingonly the Hessian or constraint Jacobian, the Jacobian of the entire nonlinearset of equations is approximated using a multisecant method. We show howpreconditioning can be incorporated into the multisecant update in order toimprove the performance of the method. For nonconvex problems, we propose asimple modification of the secant conditions to regularize the Hessian.Numerical experiments suggest that the algorithm is a promising alternative toconventional gradient-based algorithms, particularly when errors are present inthe data.

Error-tolerant Multisecant Method for Nonlinearly Constrained Optimization