New unifying convergence criteria for Newton-like methods
نویسندگان
چکیده
منابع مشابه
A Unifying Framework for Convergence Analysis of Approximate Newton Methods
Many machine learning models are reformulated as optimization problems. Thus, it is important to solve a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost in each iteration whil...
متن کاملConvergence of Newton { like
We present a (semilocal) Kantorovich{type analysis for Newton{like methods for singular operator equations using outer inverses. We establish sharp generalizations of the Kantorovich theory and the Mysovskii theory for operator equations when the derivative is not necessarily invertible. The results reduce in the case of an invertible derivative to well{known theorems of Kantorovich and Mysovsk...
متن کاملOn Semilocal Convergence of Inexact Newton Methods
Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...
متن کاملApproximate Newton Methods and Their Local Convergence
Many machine learning models are reformulated as optimization problems. Thus, it is important to solve a large-scale optimization problem in big data applications. Recently, stochastic second order methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost in each iteratio...
متن کاملConvergence rates of sub-sampled Newton methods
We consider the problem of minimizing a sum of n functions via projected iterations onto a convex parameter set C ⇢ R, where n p 1. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In this paper, we use sub-sampling techniques together with low-rank approximation to design a new randomized batch algorithm which possesses comparable convergence rate to ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicationes Mathematicae
سال: 2002
ISSN: 1233-7234,1730-6280
DOI: 10.4064/am29-3-7