TY - JOUR T1 - A Generalized Quasi-Newton Equation and Computational Experience 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.