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. Insteady Pan suggested a new equation, and showed ...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. Insteady 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.展开更多
基金Project 10371017 supported by National Natural Science Foundation of China.
文摘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. Insteady 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.
