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Applied Mathematics and Mechanics

, Volume 30, Issue 5, pp 659–668 | Cite as

An SQP algorithm for mathematical programs with nonlinear complementarity constraints

  • Zhi-bin Zhu (朱志斌)Email author
  • Jin-bao Jian (简金宝)
  • Cong Zhang (张聪)
Article

Abstract

In this paper, we describe a successive approximation and smooth sequential quadratic programming (SQP) method for mathematical programs with nonlinear complementarity constraints (MPCC). We introduce a class of smooth programs to approximate the MPCC. Using an l 1 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints (MPEC) when the algorithm terminates finitely.

Key words

mathematical programs with equilibrium constraints (MPEC) SQP algorithm successive approximation global convergence superlinear convergence rate 

Chinese Library Classification

O221 

2000 Mathematics Subject Classification

90C30 65K05 

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Copyright information

© Shanghai University and Springer-Verlag GmbH 2009

Authors and Affiliations

  • Zhi-bin Zhu (朱志斌)
    • 1
    Email author
  • Jin-bao Jian (简金宝)
    • 2
  • Cong Zhang (张聪)
    • 1
  1. 1.School of Mathematics & Computational ScienceGuilin University of Electronic TechnologyGuilinP. R. China
  2. 2.College of Mathematics and Information ScienceGuangxi UniversityNanningP. R. China

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