A smoothing newton method for semi-infinite programming

Dong Hui Li, Liqun Qi, Judy Tam, Soon Y.I. Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

41 Citations (Scopus)


This paper is concerned with numerical methods for solving a semi-infinite programming problem. We reformulate the equations and nonlinear complementarity conditions of the first order optimality condition of the problem into a system of semismooth equations. By using a perturbed Fischer-Burmeister function, we develop a smoothing Newton method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by the smoothing Newton method converges superlinearly/quadratically. Printed in the Netherlands.
Original languageEnglish
Pages (from-to)169-194
Number of pages26
JournalJournal of Global Optimization
Issue number2
Publication statusPublished - 1 Nov 2004


  • KKT condition
  • Semi-infinite programming
  • Semismooth equations
  • Smoothing Newton method

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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