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
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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
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An Algorithm without A Penalty Function or A Filter for Nonlinear Equations
More Information
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Received Date:
18/03/2017
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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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