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Volume 24, Issue 5
A Generalized Quasi-Newton Equation and Computational Experience

Lei-hong Zhang & Ping-qi Pan

J. Comp. Math., 24 (2006), pp. 665-674.

Published online: 2006-10

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  • Abstract

The quasi-Newton equation has played a central role in the quasi-Newton methods for solving systems of nonlinear equations and/or unconstrained optimization problems. Instead, Pan suggested a new equation, and showed that it is of the second order while the traditional of the first order, in certain approximation sense [12]. In this paper, we make a generalization of the two equations to include them as special cases. The generalized equation is analyzed, and new updates are derived from it. A DFP-like new update outperformed the traditional DFP update in computational experiments on a set of standard test problems.

  • Keywords

System of nonlinear equations, Unconstrained optimization, Quasi-Newton equation, Second-order Quasi-Newton equation, Update formula.

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-665, author = {Lei-hong Zhang and Ping-qi Pan}, title = {A Generalized Quasi-Newton Equation and Computational Experience}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {5}, pages = {665--674}, abstract = {

The quasi-Newton equation has played a central role in the quasi-Newton methods for solving systems of nonlinear equations and/or unconstrained optimization problems. Instead, Pan suggested a new equation, and showed that it is of the second order while the traditional of the first order, in certain approximation sense [12]. In this paper, we make a generalization of the two equations to include them as special cases. The generalized equation is analyzed, and new updates are derived from it. A DFP-like new update outperformed the traditional DFP update in computational experiments on a set of standard test problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8782.html} }
TY - JOUR T1 - A Generalized Quasi-Newton Equation and Computational Experience AU - Lei-hong Zhang & Ping-qi Pan JO - Journal of Computational Mathematics VL - 5 SP - 665 EP - 674 PY - 2006 DA - 2006/10 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8782.html KW - System of nonlinear equations, Unconstrained optimization, Quasi-Newton equation, Second-order Quasi-Newton equation, Update formula. AB -

The quasi-Newton equation has played a central role in the quasi-Newton methods for solving systems of nonlinear equations and/or unconstrained optimization problems. Instead, Pan suggested a new equation, and showed that it is of the second order while the traditional of the first order, in certain approximation sense [12]. In this paper, we make a generalization of the two equations to include them as special cases. The generalized equation is analyzed, and new updates are derived from it. A DFP-like new update outperformed the traditional DFP update in computational experiments on a set of standard test problems.

Lei-hong Zhang and Ping-qi Pan. (2006). A Generalized Quasi-Newton Equation and Computational Experience. Journal of Computational Mathematics. 24 (5). 665-674. doi:
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