The characterization of Q-superlinear convergence of methods for constrained optimization

We consider the application of a general class of quasi-Newton methods to the solution of the classical equality constrained nonlinear optimization problem. Specifically, we develop necessary and sufficient conditions for the Q-superlinear convergence of such methods and present a companion linear convergence theorem. The essential conditions relate to the manner in which the Hessian of the Lagangian function is approximated. For convex programs the Q-superlinear convergence is obtained.