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Reducing Chaos and Bifurcations in Newton-Type Methods [PDF]
Abstract and Applied Analysis, 2013 We study the dynamics of some Newton-type iterative methods when they are applied of polynomials degrees two and three. The methods are free of high-order derivatives which are the main limitation of the classical high-order iterative schemes.
Á. A. Magreñán +5 more
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On the DSM Newton-type method [PDF]
Journal of Applied Mathematics and Computing, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ramm, Alexander G., A. G. Ramm
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Projected Newton-type methods in machine learning [PDF]
, 2011 We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected ...
Sra, S., Kim, D., Schmidt, M.
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Inexact Nonconvex Newton-Type Methods [PDF]
INFORMS Journal on Optimization, 2021 The paper aims to extend the theory and application of nonconvex Newton-type methods, namely trust region and cubic regularization, to the settings in which, in addition to the solution of subproblems, the gradient and the Hessian of the objective function are approximated. Using certain conditions on such approximations, the paper establishes optimal
Zhewei Yao +3 more
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Newton-type multilevel optimization method [PDF]
Optimization Methods and Software, 2019 Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the optimization model, and as a result, they outperform single-level methods, especially for large-scale models.
Chin Pang Ho +2 more
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Gauss–Newton-type methods for bilevel optimization [PDF]
Computational Optimization and Applications, 2021 AbstractThis article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions.
Jörg Fliege +2 more
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A Newton‐type method and its application [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We prove an existence and uniqueness theorem for solving the operator equation F(x) + G(x) = 0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified ...
V. Antony Vijesh, P. V. Subrahmanyam
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Hybrid Newton-type method for a class of semismooth equations [PDF]
, 2002 In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct ...
Pieraccini, Sandra
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Newton-type methods for simultaneous matrix diagonalization
Calcolo, 2022 This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equations associated to this problem, we construct a sequence that converges quadratically towards the ...
Rima Khouja +2 more
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Journal of Complexity, 2010 Inexact Newton-type methods are discussed for approximating a locally unique solution of the nonlinear equation \(A(x)^{\#}(F(x)+G(x))=0\) in Banach space. Here \(F\) is a Fréchet-differentiable operator, \(G\) is a continuous operator and \(A(x)^{\#}\) is an analog of the Moore-Penrose generalized inverse of \(A(x)\) which is an approximation of the ...
Ioannis K. Argyros, Saïd Hilout
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