On the local and global convergence of a reduced Quasi-Newton method 1

In optimization in with m nonlinear equality constraints, we study the local convergence of reduced quasi-Newton methods, in which the updated matrix is of order n−m Furthermore, we give necessary and sufficient conditions for superlinear convergence (in one step) and we introduce 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 we give conditions so that asymptotically the step-size will be equal to one.