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On the restricted step method coupled with the augmented Hessian for the search of stationary points of any continuous function
Author(s) -
Anglada Josep Maria,
Bofill Josep Maria
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)62:2<153::aid-qua3>3.0.co;2-v
Subject(s) - hessian matrix , maxima and minima , saddle point , hessian equation , convergence (economics) , stationary point , function (biology) , mathematical optimization , mathematics , quasi newton method , order (exchange) , computer science , algorithm , newton's method , mathematical analysis , geometry , physics , partial differential equation , nonlinear system , evolutionary biology , first order partial differential equation , biology , finance , quantum mechanics , economics , economic growth
In any optimization using the augmented Hessian technique, the step is not restricted to any length. Since the restriction of the step at each iteration is very important in order to achieve good convergence, we present a coupled method such that the augmented Hessian automatically gives both the adequate length of the step and the correct Hessian structure. The method is showed for the minima and saddle points of any order. © 1997 John Wiley & Sons, Inc.