On Smoothing l1 Exact Penalty Function for Nonlinear Constrained Optimization Problems

doi:10.1007/s40305-024-00566-9

Journal of the Operations Research Society of China ›› 2026, Vol. 14 ›› Issue (2): 700-718.doi: 10.1007/s40305-024-00566-9

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On Smoothing l₁ Exact Penalty Function for Nonlinear Constrained Optimization Problems

Yu-Fei Ren, You-Lin Shang

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, Henan, China

Received:2023-12-29 Revised:2024-08-27 Online:2026-06-30 Published:2026-07-06
Contact: You-Lin Shang E-mail:mathshang@sina.com
Supported by:
You-Lin Shang’ work was supported by the National Natural Science Foundation of China (Nos.11471102 and 12071112) and Basic Research Projects for Key Scientific Research Projects of Henan Projects of China (No.20ZX001).

Abstract

Abstract: The penalty function method is a significant method for solving nonlinear constrained optimization problems (COP). In this paper, a new quadratic continuous differentiable smooth penalty function is proposed for the l₁ exact penalty function. The error estimations between the objective function values of the smooth penalty problem, the penalty problem and the original problem are also studied. Furthermore, based on the smoothed penalty function, an algorithm for solving COP is proposed, and the convergence of the algorithm is proved. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.

Key words: l₁ exact penalty function, Constrained optimization problem, Smoothing method, Approximate optimal solution

CLC Number:

90C30

Yu-Fei Ren, You-Lin Shang. On Smoothing l₁ Exact Penalty Function for Nonlinear Constrained Optimization Problems[J]. Journal of the Operations Research Society of China, 2026, 14(2): 700-718.

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URL: https://www.jorsc.shu.edu.cn/EN/10.1007/s40305-024-00566-9

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On Smoothing l₁ Exact Penalty Function for Nonlinear Constrained Optimization Problems

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