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2018 Volume 43 Issue 5
Article Contents

FANG Yue-hua. An Algorithm without A Penalty Function or A Filter for Nonlinear Equations[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(5): 23-30. doi: 10.13718/j.cnki.xsxb.2018.05.005
Citation: FANG Yue-hua. An Algorithm without A Penalty Function or A Filter for Nonlinear Equations[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(5): 23-30. doi: 10.13718/j.cnki.xsxb.2018.05.005

An Algorithm without A Penalty Function or A Filter for Nonlinear Equations

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  • Received Date: 18/03/2017
  • We present a new algorithm for solving a system of nonlinear equations. The system of nonlinear equations is reformulated into a nonlinear programming problem firstly, and then we solve the problem by a method without a penalty function or a filter. Under the standard assumption that Jacobi matrices are uniformly full rank, it is proved that every limit point of the sequence generated by the algorithm is a solution of the system of nonlinear equations. Introducing the second-order correction technique to the algorithm for overcoming the so-called Maratos effect, this algorithm will locally have superlinear convergence.
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An Algorithm without A Penalty Function or A Filter for Nonlinear Equations

Abstract: We present a new algorithm for solving a system of nonlinear equations. The system of nonlinear equations is reformulated into a nonlinear programming problem firstly, and then we solve the problem by a method without a penalty function or a filter. Under the standard assumption that Jacobi matrices are uniformly full rank, it is proved that every limit point of the sequence generated by the algorithm is a solution of the system of nonlinear equations. Introducing the second-order correction technique to the algorithm for overcoming the so-called Maratos effect, this algorithm will locally have superlinear convergence.

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