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

Gilbert, J.-C. (1989). On the local and global convergence of a reduced Quasi-Newton method1. Optimization 20 (4) 421-450. 10.1080/02331938908843462.

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	constrained optimization, successive quadratic programming, reduced quasi-newton method, superlinear convergence, exact penalty function, are search, step-size selection procedure, global convergence,
Research Programs:	System and Decision Sciences - Core (SDS)
Depositing User:	Romeo Molina
Date Deposited:	20 Apr 2016 07:30
Last Modified:	27 Aug 2021 17:26
URI:	https://pure.iiasa.ac.at/12800

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