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A Special Newton-Type Optimization Method
Optimization, 1992The Kuhn–Tucker conditions of an optimization problem with inequality constraints are transformed equivalently into a special nonlinear system of equations T 0(z) = 0. It is shown that Newton's method for solving this system combines two valuable properties: The local Q-quadratic convergence without assuming the strict complementary slackness condition
Andreas Fischer
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Interval methods of Newton type for nonlinear equations
Es sei f:[a,b]\(\subset {\mathbb{R}}\to {\mathbb{R}}\); zu bestimmen ist eine Nullstelle \(x^*\in [a,b]\) mit \(f(x^*)=0\). Dazu werden zwei Intervall- Newton-Verfahren angegeben und ihre Verwirklichung durch eine passende, einseitig rundende Computer-Arithmetik beschrieben.
Dimitrova, Neli S., Markov, Svetoslav M.
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On an Aitken–Newton type method
Numerical Algorithms, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ion Pavaloiu, Emil Catinas
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Newton-Type Methods: A Broader View
Journal of Optimization Theory and Applications, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexey F. Izmailov, Mikhail V. Solodov
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Newton-type method for solving generalized inclusion
Numerical Algorithms, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paulo Sérgio Marques dos Santos +2 more
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Slope tests for newton-type methods
Applied Mathematics and Computation, 1992Suppose we are given a function \(f: \mathbb{R}^ n\to\mathbb{R}^ n\), with \(f\in C^ 1(D)\), \(D\subseteq\mathbb{R}^ n\). \textit{M. C. Pandian} [SIAM J. Numer. Anal. 22, 779-791 (1985; Zbl 0586.65041)] gave existence and uniqueness tests for a zero \(x^*\) of \(f\) in a rectangular subset \(X\subset D\).
Shen, Zuhe, Wolfe, M. A.
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Newton-Type Methods for Quasidifferentiable Equations
Journal of Optimization Theory and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, L. W., Xia, Z. Q.
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A quasi-Newton type method for equilibrium problems
Numerical Algorithms, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Leonardo A. Sousa +3 more
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