Choosing the Forcing Terms in an Inexact Newton Method
نویسندگان
چکیده
An inexact Newton method is a generalization ofNewton's method for solving F(x) 0, F n _ _ in, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition F (x) + F'(xk) sk _< F(x)II for a "forcing term" r/ [0, 1). In typical applications, the choice of the forcing terms is critical to the efficiency of the method and can affect robustness as well. Promising choices of the forcing terms are given, their local convergence properties are analyzed, and their practical performance is shown on a representative set of test problems.
منابع مشابه
Global convergence of an inexact interior-point method for convex quadratic symmetric cone programming
In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programmin...
متن کاملOn the Convergence of Inexact Newton Methods
A solid understanding of convergence behaviour is essential to the design and analysis of iterative methods. In this paper we explore the convergence of inexact iterative methods in general, and inexact Newton methods in particular. A direct relationship between the convergence of inexact Newton methods and the forcing terms is presented in both theory and numerical experiments.
متن کاملJacobian Smoothing Inexact Newton Method for Ncp with a Special Choice of Forcing Parameters
The inexact Newton method with a special choice of forcing parameters is proposed for solving nonlinear complementarity problems. This method belongs to the class of Jacobian smoothing methods. Linear system is solved approximately in every iteration. The sequence of forcing terms controls the accuracy level of the approximate solution and influences the behavior of the method. Globalization st...
متن کاملInexact Newton methods for model simulation
Robust and efficient solution techniques for solving macroeconometric models are increasingly becoming a key factor in developing models employed by policy-making institutions for policy simulations and forecasting. Traditionally, when solved in presence of forward-looking variables, these models are nonlinear, large-scale and sparse and give rise to large and highly structured nonlinear system...
متن کاملGlobally Convergent Inexact Newton Methods
Inexact Newton methods for finding a zero of F 1 1 are variations of Newton's method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local linear model of F. Here, inexact Newton methods are formulated that incorporate features designed to improve convergence from arbitrary starting points. For each method, a basic global convergence ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 17 شماره
صفحات -
تاریخ انتشار 1996