Partial augmented lagrangian method and mathematical programs with complementarity constraints

X. X. Huang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

In this paper, we apply a partial augmented Lagrangian method to mathematical programs with complementarity constraints (MPCC). Specifically, only the complementarity constraints are incorporated into the objective function of the augmented Lagrangian problem while the other constraints of the original MPCC are retained as constraints in the augmented Lagrangian problem. We show that the limit point of a sequence of points that satisfy second-order necessary conditions of the partial augmented Lagrangian problems is a strongly stationary point (hence a B-stationary point) of the original MPCC if the limit point is feasible to MPCC, the linear independence constraint qualification for MPCC and the upper level strict complementarity condition hold at the limit point. Furthermore, this limit point also satisfies a second-order necessary optimality condition of MPCC. Numerical experiments are done to test the computational performances of several methods for MPCC proposed in the literature.
Original languageEnglish
Pages (from-to)235-254
Number of pages20
JournalJournal of Global Optimization
Volume35
Issue number2
DOIs
Publication statusPublished - 1 Jun 2006

Keywords

  • B-stationarity
  • Constraint qualification
  • Mathematical programs with complementarity constraints
  • Optimality conditions
  • Partial augmented Lagrangian method

ASJC Scopus subject areas

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

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