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An SQP algorithm for mathematical programs with nonlinear complementarity constraints

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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.

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References

  1. Outrate, J. V., Kocvare, M., and Zowe, J. Nonsmooth Approach to Optimization Problems with Equilibrium Consraints, Kluwer Academic Publishers, The Netherlands (1998)

    Google Scholar 

  2. Jiang, H. and Ralph, D. Smooth SQP method for mathematical programs with nonlinear complementarity constraints. SIAM Journal on Optimization 10, 779–808 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fukushima, M., Luo, Z. Q., and Pang, J. S. A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints. Computational Optimization and Applications 10, 5–34 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ma, C. F. and Liang, G. P. A new successive approximation damped Newton method for nonlinear complementarity problems. Journal of Mathematical Research and Exposition 23, 1–6 (2003)

    MATH  MathSciNet  Google Scholar 

  5. Zhu, Z. B, Luo, Z. J., and Zeng, J. W. A new smoothing technique for mathematical programs with equilibrium constraints. Appl. Math. Mech. -Engl. Ed. 28(10), 1407–1414 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fukushima, M. and Pang, J. S. Some feasibility issues in mathematical programs with equilibrium constraints. SIAM Journal on Optimization 8, 673–681 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Panier, E. R. and Tits, A. L. On combining feasibility, descent and superlinear convergence in inequality constrained optimization. Mathematical Programming 59, 261–276 (1993)

    Article  MathSciNet  Google Scholar 

  8. Zhu, Z. B. and Zhang, K. C. A superlinearly convergent SQP algorithm for mathematical programs with linear complementarity constraints. Applied Mathematics and Computation 172, 222–244 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Panier, E. R. and Tits, A. L. A superlinearly convergent feasible method for the solution of inequality constrained optimization problems. SIAM Journal on Control and Optimization 25, 934–950 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Facchinei, F. and Lucidi, S. Quadraticly and superlinearly convergent for the solution of inequality constrained optimization problem. Journal of Optimization Theory and Applications 85, 265–289 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics & Computational Science, Guilin University of Electronic Technology, Guilin, 541004, Guangxi Province, P. R. China

    Zhi-bin Zhu  (朱志斌) & Cong Zhang  (张聪)

  2. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, P. R. China

    Jin-bao Jian  (简金宝)

Authors
  1. Zhi-bin Zhu  (朱志斌)
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  2. Jin-bao Jian  (简金宝)
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  3. Cong Zhang  (张聪)
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Corresponding author

Correspondence to Zhi-bin Zhu  (朱志斌).

Additional information

(Communicated by Shi-sheng ZHANG)

Project supported by the National Natural Science Foundation of China (Nos. 10501009, 10771040), the Natural Science Foundation of Guangxi Province of China (Nos. 0728206, 0640001), and the China Postdoctoral Science Foundation (No. 20070410228)

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Zhu, Zb., Jian, Jb. & Zhang, C. An SQP algorithm for mathematical programs with nonlinear complementarity constraints. Appl. Math. Mech.-Engl. Ed. 30, 659–668 (2009). https://doi.org/10.1007/s10483-009-0512-x

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  • DOI: https://doi.org/10.1007/s10483-009-0512-x

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2000 Mathematics Subject Classification

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