منابع مشابه
Globally 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 ...
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A new smoothing algorithm for the solution of nonlinear complementarity problems (NCP) is introduced in this paper. It is based on semismooth equation reformulation of NCP by Fischer–Burmeister function and its related smooth approximation. In each iteration the corresponding linear system is solved only approximately. Since inexact directions are not necessarily descent, a nonmonotone techniqu...
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Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the computations and/or to implicitly implement a form of statistical regularization. In this paper, we consider second-order iterative optimization algorithms, i.e., thos...
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The dogleg method is a classical trust-region technique for globalizing Newton’s method. While it is widely used in optimization, including large-scale optimization via truncatedNewton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexac...
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In inexact Newton methods for solving nonlinear systems of equations, an approximation to the step sk of the Newton’s system J (xk)s =−F(xk) is found. This means that sk must satisfy a condition like ‖F(xk) + J (xk)sk‖ ≤ ηk‖F(xk)‖ for a forcing term ηk ∈ [0,1). Possible choices for ηk have already been presented. In this work, a new choice for ηk is proposed. The method is globalized using a ro...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 1994
ISSN: 1052-6234,1095-7189
DOI: 10.1137/0804022