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Generalized Newton Method for a Kind of Complementarity Problem [PDF]
Abstract and Applied Analysis, 2014 A generalized Newton method for the solution of a kind of complementarity problem is given. The method is based on a nonsmooth equations reformulation of the problem by F-B function and on a generalized Newton method.
Shou-qiang Du
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A generalized multivariable Newton method [PDF]
Fixed Point Theory and Algorithms for Sciences and Engineering, 2021 AbstractIt is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution.
Regina S. Burachik +2 more
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A Newton-type technique for solving absolute value equations
Alexandria Engineering Journal, 2023 The Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson’s method. Convergence results are established under
Alamgir Khan +7 more
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Approximations and generalized Newton methods [PDF]
Mathematical Programming, 2017 We present approaches to (generalized) Newton methods in the framework of generalized equations $0\in f(x)+M(x)$, where $f$ is a function and $M$ is a multifunction. The Newton steps are defined by approximations $\hat f$ of $f$ and the solutions of $0\in \hat{f}(x)+M(x)$.
Diethard Klatte, Bernd Kummer
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Local convergence of the Gauss-Newton-Kurchatov method under generalized Lipschitz conditions
Karpatsʹkì Matematičnì Publìkacìï, 2021 We investigate the local convergence of the Gauss-Newton-Kurchatov method for solving nonlinear least squares problems. This method is a combination of Gauss-Newton and Kurchatov methods and it is used for problems with the decomposition of the operator.
S.M. Shakhno, H.P. Yarmola
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Extended Newton-type Method for Generalized Equations with Hölderian Assumptions
Communications in Advanced Mathematical Sciences, 2021 In the present paper, we consider the generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable on a neighborhood $\Omega$ of a point $\bar{x}$ in $\mathcal X$, $g:\mathcal X\to \mathcal Y$ is ...
Mohammed Harunor Rashid +1 more
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Correction to: Approximations and generalized Newton methods [PDF]
Mathematical Programming, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diethard Klatte, Bernd Kummer
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Journal of Mathematics, 2021 The preconditioned generalized shift-splitting (PGSS) iteration method is unconditionally convergent for solving saddle point problems with nonsymmetric coefficient matrices.
Yao Xiao, Qingbiao Wu, Yuanyuan Zhang
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A New Efficient Method for Absolute Value Equations
Mathematics, 2023 In this paper, the two-step method is considered with the generalized Newton method as a predictor step. The three-point Newton–Cotes formula is taken as a corrector step. The proposed method’s convergence is discussed in detail.
Peng Guo +5 more
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A Generalized Newton Method for Subgradient Systems
Mathematics of Operations Research, 2023 This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second order subdifferential of such functions that enjoy extensive calculus rules and can be efficiently computed for broad classes
Pham Duy Khanh +2 more
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