A Superlinearly Convergent Sequential Quadratically Constrained Quadratic Programming Algorithm for Degenerate Nonlinear Programming

We present an algorithm that achieves superlinear convergence for nonlinear programs satisfying the Mangasarian-Fromovitz constraint qualiication and the quadratic growth condition. This convergence result is obtained despite the potential lack of a locally convex augmented Lagrangian. The algorithm solves a succession of subproblems that have quadratic objective and quadratic constraints, both possibly nonconvex. By the use of a trust-region constraint we guarantee that any stationary point of the subproblem induces superlinear convergence which avoids the problem of computing a global minimum.