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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (5): 659-668.doi: https://doi.org/10.1007/s10483-009-0512-x

• Articles • 上一篇    下一篇

An SQP algorithm for mathematical programs with nonlinear complementarity constraints

朱志斌1 简金宝2 张聪1   

  1. 1. School of Mathematics & Computational Science, Guilin University of Electronic Technology,Guilin 541004, Guangxi Province, P. R. China;
    2. College of Mathematics and Information Science, Guangxi University,Nanning 530004, P. R. China
  • 收稿日期:2008-05-02 修回日期:2009-02-22 出版日期:2009-05-01 发布日期:2009-05-01

An SQP algorithm for mathematical programs with nonlinear complementarity constraints

Zhi-Bin ZHU1, Jin-Bao JIAN2, Cong ZHANG1   

  1. 1. School of Mathematics & Computational Science, Guilin University of Electronic Technology,Guilin 541004, Guangxi Province, P. R. China;
    2. College of Mathematics and Information Science, Guangxi University,Nanning 530004, P. R. China
  • Received:2008-05-02 Revised:2009-02-22 Online:2009-05-01 Published:2009-05-01

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摘要： 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 l1 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.

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 l1 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.

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