Lower-order penalty methods for mathematical programs with complementarity constraints

Xiaoqi Yang, X. X. Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


In this article, a smooth mathematical program with complementarity constraints (MPCC) is reformulated as a non-smooth constrained optimization problem by using the Fischer-Burmeister function. A lower-order penalty method is applied to transform the resulted constrained optimization problem into unconstrained optimization problems. Lower-order penalty functions may not be locally Lipschitz. However, they require weaker conditions to guarantee an exact penalization property than the classical l1penalty functions. We derive optimality conditions for the penalty problems using a smooth approximate variational principle, and establish that the limit point of a sequence of points that satisfy the second-order necessary optimality conditions of penalty problems is a strongly stationary point (hence a B-stationary point) of the original MPCC if the limit point is feasible to MPCC, and a linear independence constraint qualification for MPCC and an upper level strict complementarity condition hold at the limit point. Furthermore, the limit point also satisfies a second-order necessary condition of MPCC. Numerical examples are presented to demonstrate and compare the effectiveness of the proposed methods.
Original languageEnglish
Pages (from-to)693-720
Number of pages28
JournalOptimization Methods and Software
Issue number6
Publication statusPublished - 1 Dec 2004


  • B-stationary point
  • Convergence
  • Mathematical program with complementarity constraints
  • Optimality condition
  • Penalty function

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics


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