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 qualification 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. 1. Introduction. Recently, there has been renewed interest in analyzing and modifying the algorithms for constrained nonlinear optimization for cases where the traditional regularity conditions do not hold [5, 12, 11, 20, 24, 23]. This research has been motivated by the fact that large-scale nonlinear programming problems tend to be almost degenerate (have large condition numbers for the Jac..