Results 1 to 10 of about 243 (114)
On a Semismooth* Newton Method for Solving Generalized Equations
SIAM Journal on Optimization, 2021 In the paper, a Newton-type method for the solution of generalized equations (GEs) is derived, where the linearization concerns both the single-valued and the multi-valued part of the considered GE. The method is based on the new notion of semismoothness${}^*$ which, together with a suitable regularity condition, ensure the local superlinear ...
Helmut Gfrerer, Jiří V Outrata
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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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