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Remarks on the updated Hessian matrix methods
Author(s) -
Bofill Josep Maria
Publication year - 2003
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/qua.10709
Subject(s) - hessian matrix , saddle point , quasi newton method , mathematics , saddle , hessian equation , matrix exponential , matrix (chemical analysis) , exponential function , broyden–fletcher–goldfarb–shanno algorithm , order (exchange) , minification , newton's method , set (abstract data type) , function (biology) , mathematical optimization , computer science , mathematical analysis , nonlinear system , geometry , physics , materials science , asynchronous communication , first order partial differential equation , computer network , partial differential equation , composite material , quantum mechanics , programming language , differential equation , finance , economics , biology , evolutionary biology
Abstract Optimizing a function with respect to a set of variables using the quasi‐Newton–Raphson method implies updating the Hessian matrix at each iteration. The Broyden–Fletcher–Goldfarb–Shanno update formula is used for minimization and the Murtagh–Sargent–Powell update formula for optimization of first‐order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first‐order saddle points. The second formula is a modification of the TS–Broyden–Fletcher–Goldfarb–Shanno update and could used for both minimum and first‐order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden–Fletcher–Goldfarb–Shanno and Murtagh–Sargent–Powell formulae. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 324–332, 2003