Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization

Gui Hua Lin, Xiaojun Chen, Masao Fukushima

Research output: Journal article publicationJournal articleAcademic researchpeer-review

40 Citations (Scopus)


In this paper, we consider the stochastic mathematical programs with linear complementarity constraints, which include two kinds of models called here-and-now and lower-level wait-and-see problems. We present a combined smoothing implicit programming and penalty method for the problems with a finite sample space. Then, we suggest a quasi-Monte Carlo approximation method for solving a problem with continuous random variables. A comprehensive convergence theory is included as well. We further report numerical results with the so-called picnic vender decision problem.
Original languageEnglish
Pages (from-to)343-368
Number of pages26
JournalMathematical Programming
Issue number1-2
Publication statusPublished - 1 Jan 2009
Externally publishedYes


  • Here-and-now
  • Quasi-Monte Carlo method
  • Smoothing implicit programming
  • Stochastic mathematical program with equilibrium constraints
  • Wait-and-see

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research
  • Software
  • Computer Graphics and Computer-Aided Design
  • Computer Science(all)

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