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<p>In this paper, a nonmonotone smoothing Newton method is proposed for solving systems of non-linear equalities and inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations. A smoothing Newton method is developed for solving the systems of nonlinear equalities and inequalities by adopting a modified nonmontone line search technique. And the global and local superlinear convergence of the algorithm are proved under mild assumptions. The preliminary numerical results are reported.</p>

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A Nonmonotone Smoothing Newton Method for Systems of Nonlinear Equalities and Inequalities Based on a New Smoothing Function

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Liu-yang Yuan,
  • Fei Cui,
  • Zhong-ping Wan,
  • Zi-yue Wang

摘要

In this paper, a nonmonotone smoothing Newton method is proposed for solving systems of non-linear equalities and inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations. A smoothing Newton method is developed for solving the systems of nonlinear equalities and inequalities by adopting a modified nonmontone line search technique. And the global and local superlinear convergence of the algorithm are proved under mild assumptions. The preliminary numerical results are reported.