In optimization in ℝn with m nonlinear equality constraints, the author studies the local convergence of reduced quasi-Newton methods, in which the updated matrix is of order n-m. Furthermore, he gives necessary and sufficient conditions for superlinear convergence (in one step) and introduces a device to globalize the local algorithm. It consists in determining a step along an arc in order to decrease an exact penalty function and the author gives conditions so that asymptotically the step-size will be equal to one.
