On Smoothing l 1 Exact Penalty Function for Constrained Optimization Problems

Xinsheng Xu, Chuangyin Dang, Felix T.S. Chan, Yongli Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


This article introduces a smoothing technique to the l 1 exact penalty function. An application of the technique yields a twice continuously differentiable penalty function and a smoothed penalty problem. Under some mild conditions, the optimal solution to the smoothed penalty problem becomes an approximate optimal solution to the original constrained optimization problem. Based on the smoothed penalty problem, we propose an algorithm to solve the constrained optimization problem. Every limit point of the sequence generated by the algorithm is an optimal solution. Several numerical examples are presented to illustrate the performance of the proposed algorithm.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalNumerical Functional Analysis and Optimization
Issue number1
Publication statusPublished - 2 Jan 2019


  • Constrained optimization problems
  • l exact penalty function
  • smoothing technique

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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