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Interval Relaxation Method for Linear Complementarity Problem

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

This paper established an interval relaxation method for complementarity problems. We proposed a method for linear complementarity problems, which M is assumed to be an H-matrix with a positive main diagonal. The convergence of these algorithms are proved. Numerical results are presented and show that the algorithms are stable and efficient.

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References

  1. Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Academic press, New York (1983)

    MATH  Google Scholar 

  2. Fathi, Y.: Computational Complexity of linear complementarity problems associated with positive definite Matices. Math. Programming 17, 335–344 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Han, C., Cao, D., Qin, J.: An interval method for vertical nonlinear complementarity problems. Journal of Nanjing University Mathematical Biquarterly 27(1), 75–81 (2010)

    MathSciNet  Google Scholar 

  4. Gotz, A., Wang, Z., Shen, Z.: Enclosing solution of linear complementarity problems for H-matrix. Reliable Computing 10(6), 423–435 (2004)

    Article  MathSciNet  Google Scholar 

  5. Lei, J.: Matric and Application. Mechanical and Industry press, Beijing (2005)

    Google Scholar 

  6. Moore, R.E.: Interval Analysis. Prentice-Hall, New Jersey (1966)

    MATH  Google Scholar 

  7. Moore, R.E.: A test for existence of solutions to nonlinear systems. SIAM J Numer Anal. 14, 611–615 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)

    MATH  Google Scholar 

  9. Murty, K.G.: Linear Complementarity, Linear and Nonlinear Programming. Hedermann, Berlin (1988)

    MATH  Google Scholar 

  10. Rui, W., Cao, D., Zhang, Z.: An interval method for the P0-matrix linear complementarity problem. Journal of Nanjing University Mathematical Biquarterly 24(2), 344–350 (2007)

    MATH  Google Scholar 

  11. Wang, D.: The Method for Nonlinear Equations. Science and Technolegy press, Shang Hai (1987)

    Google Scholar 

  12. Zhao, X.: Homophony method for solving horizontal linear complementarity problem. Journal of Jilin University (Science Edition) 48(5), 766–770 (2010)

    MathSciNet  Google Scholar 

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Jiang, J. (2011). Interval Relaxation Method for Linear Complementarity Problem. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_79

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_79

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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