# Solving Nonlinear Equations

@article{Hornberger2013SolvingNE, title={Solving Nonlinear Equations}, author={George M. Hornberger and Patricia L. Wiberg}, journal={Advanced Optimization for Process Systems Engineering}, year={2013} }

. The paper is devoted to the study of a system of nonlinear integral equations. First, this system is reduced to a ﬁ xed point problem of a nonlinear integral operator and hence we can give suitable assumptions and using a ﬁ xed point theorem of Krasnosel’skii type in order to obtain the existence of solutions. Next, we prove the existence of asymptotically stable solutions for the above system. In order to illustrate the results, an example is also presented.

## 31 Citations

Regularization path-following methods with the trust-region updating strategy for linear complementarity problems

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It is shown that, starting from a multiple of the positive eigenvector of A, the Newton-like iteration for this nonlinear eigen-problem Ax+ F(x) = λx converges monotonically.

On convergence properties of the modified trust region method under Hölderian error bound condition

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Trust region method is one of the important methods for nonlinear equations. In this paper, we show that the modified trust region method converges globally under the Hölderian continuity of the…

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- Computer ScienceArXiv
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Numerical results show that the proposed method is quite reliable to find the global optimal point of the unconstrained optimization problem, compared to the multi-start method (the built-in subroutine GlobalSearch.m of the MATLAB R2020a environment).

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Numerical results show that the proposed continuation Newton method with the deflation technique performs well for the large-scale global optimization problems, especially the problems of which are difficult to be solved by the known global optimization methods.

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The generalized continuation Newton method and the trust-region updating strategy for the underdetermined system of nonlinear equations is considered and is shown to be more robust and faster than the traditional optimization method such as the Levenberg-Marquardt method.

Extended Local Convergence for High Order Schemes Under ω-Continuity Conditions

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Gus Argyros, Michael Argyros, Ioannis K. Argyros, Santhosh George Department of Computing and Technology, Cameron University, Lawton, Oklahoma, USA Department of Computing and Technology, Cameron…

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The sigmoid polynomials combining - numbers and various properties of their polynomials are thoroughly presented in this paper. Based on several properties of - numbers, we derive some identities of…