Results 1 to 10 of about 219 (94)
Reducing Chaos and Bifurcations in Newton-Type Methods
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.
S. Amat, S. Busquier, Á. A. Magreñán
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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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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, Andrey Tin, Alain Zemkoho
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Order of Convergence and Dynamics of Newton–Gauss-Type Methods
Fractal and Fractional, 2023 On the basis of the new iterative technique designed by Zhongli Liu in 2016 with convergence orders of three and five, an extension to order six can be found in this paper. The study of high-convergence-order iterative methods under weak conditions is of
Ramya Sadananda +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.
Ho, CP, Kocvara, M, Parpas, P
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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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A Combined Conjugate Gradient Quasi-Newton Method with Modification BFGS Formula
International Journal of Analysis and Applications, 2023 The conjugate gradient and Quasi-Newton methods have advantages and drawbacks, as although quasi-Newton algorithm has more rapid convergence than conjugate gradient, they require more storage compared to conjugate gradient algorithms.
Mardeen Sh. Taher, Salah G. Shareef
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Mathematics, 2023 In recent years, some Newton-type schemes with noninteger derivatives have been proposed for solving nonlinear transcendental equations by using fractional derivatives (Caputo and Riemann–Liouville) and conformable derivatives.
Giro Candelario +3 more
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Newton-Type Methods for Solution of the Electric Network Equations
Trends in Computational and Applied Mathematics, 2002 Electric newtork equations give rise to interesting mathematical models that must be faced with efficient numerical optimization techniques. Here, the classical power flow problem represented by a nonlinear system of equations is solved by inexact Newton
L.V. BARBOSA +2 more
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On the Convergence Rate of Quasi-Newton Methods on Strongly Convex Functions with Lipschitz Gradient
Mathematics, 2023 The main results of the study of the convergence rate of quasi-Newton minimization methods were obtained under the assumption that the method operates in the region of the extremum of the function, where there is a stable quadratic representation of the ...
Vladimir Krutikov +3 more
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