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Abstract
QuasiNewton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence is also examined and proven to be improving with the rate of convergence of the underlying iterates. The theory is confirmed by some numerical experiments that also show the convergence of the Hessian approximations to be substantially slower for other known quasiNewton formulae. © 1991 The Mathematical Programming Society, Inc.
Original language  English 

Pages (fromto)  177195 
Number of pages  19 
Journal  Mathematical Programming 
Volume  50 
Issue number  13 
DOIs  
Publication status  Published  1 Apr 1991 
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LANCELOT: LANCELOT, a package for the solution of largescale nonlinear optimization problems
TOINT, P., Sartenaer, A., Gould, N. I. M. & Conn, A.
1/09/87 → 1/09/00
Project: Research