%0 Journal Article
%@ 0233-1934
%A Gilbert, J.-C.
%D 1989
%F iiasa:14072
%I Taylor and Francis Ltd.
%J Optimization
%N 4
%P 421-450
%R 10.1080/02331938908843462
%T On the local and global convergence of a reduced Quasi-Newton method1
%U https://pure.iiasa.ac.at/id/eprint/14072/
%V 20
%X In optimization in Rn 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. © 1989, Taylor & Francis Group, LLC.