A smoothing method for mathematical programs with equilibrium constraints

Francisco Facchinei, Houyuan Jiang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

233 Citations (Scopus)


The mathematical program with equilibrium constraints (MPEC) is an optimization problem with variational inequality constraints. MPEC problems include bilevel programming problems as a particular case and have a wide range of applications. MPEC problems with strongly monotone variational inequalities are considered in this paper. They are transformed into an equivalent one-level nonsmooth optimization problem. Then, a sequence of smooth, regular problems that progressively approximate the nonsmooth problem and that can be solved by standard available software for constrained optimization is introduced. It is shown that the solutions (stationary points) of the approximate problems converge to a solution (stationary point) of the original MPEC problem. Numerical results showing viability of the approach are reported.
Original languageEnglish
Pages (from-to)107-134
Number of pages28
JournalMathematical Programming, Series B
Issue number1
Publication statusPublished - 1 Dec 1999
Externally publishedYes


  • Equilibrium constraints
  • Global convergence
  • Optimality conditions
  • Strong monotonicity
  • Variational inequality problems

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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