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<p>In this paper, we propose two new smoothing approximation to the lower order exact penalty functions for nonlinear optimization problems with inequality constraints. Firstly, the error estimation between smoothed penalty function, non-smooth penalty function and original function is investigated. By using these new smooth penalty functions, nonlinear optimization problems with inequality constraints are transformed into unconstrained optimization problems. Then, based on each smoothed penalty function, we propose an algorithm to find the approximate optimal solution of the original constrained optimization problem, and prove the convergence of the proposed algorithm. The effectiveness of the smoothed penalty function is demonstrated through numerical examples, indicating that the algorithm is effective.</p>

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Smoothing approach of lower order exact penalty function for nonlinear constrained optimization problems

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Yufei Ren,
  • Youlin Shang,
  • Zhixian Zhang,
  • Zihao Jia

摘要

In this paper, we propose two new smoothing approximation to the lower order exact penalty functions for nonlinear optimization problems with inequality constraints. Firstly, the error estimation between smoothed penalty function, non-smooth penalty function and original function is investigated. By using these new smooth penalty functions, nonlinear optimization problems with inequality constraints are transformed into unconstrained optimization problems. Then, based on each smoothed penalty function, we propose an algorithm to find the approximate optimal solution of the original constrained optimization problem, and prove the convergence of the proposed algorithm. The effectiveness of the smoothed penalty function is demonstrated through numerical examples, indicating that the algorithm is effective.