On the local and global convergence of a reduced Quasi-Newton method1

1 January 1989

journal article
research article
Published by Taylor & Francis in Optimization

Vol. 20 (4) , 421-450
https://doi.org/10.1080/02331938908843462

Abstract

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.

Keywords

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