A sequential smooth penalization approach to mathematical programs with complementarity constraints

X. X. Huang, Xiaoqi Yang, D. L. Zhu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


In this paper, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained mathematical program via the Fischer-Burmeister function. Smooth penalty functions are used to treat this nonsmooth constrained program. Under linear independence constraint qualification, and upper level strict complementarity condition, together with some other mild conditions, we prove that the limit point of stationary points satisfying second-order necessary conditions of unconstrained penalized problems is a strongly stationary point, hence a B-stationary point of the original MPCC. Furthermore, this limit point also satisfies a second-order necessary condition of the original MPCC. Numerical results are presented to test the performance of this method.
Original languageEnglish
Pages (from-to)71-98
Number of pages28
JournalNumerical Functional Analysis and Optimization
Issue number1
Publication statusPublished - 1 Jan 2006


  • B-stationary point
  • Complementarity constraints
  • Linear independence constraint qualification
  • Mathematical program
  • Optimality condition
  • Penalty function

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization


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