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A Continuation Method for the Linear Second-Order Cone Complementarity Problem

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Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3483))

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Abstract

We reformulate the linear second-order cone complementarity problem into a system of nonlinear equations. Our reformulation is different from others. Our algorithm for the reformulation can start from an arbitrary point. We prove that our algorithm approximates an optimum of the linear second-order cone complementarity problem in finite steps under certain conditions. Finally, we show that the system of nonlinear equations of our reformulation is nonsingular at optimum under certain conditions.

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References

  1. Alizadeh, F., Goldfarb, D.: Second-order cone programming. Math. Program 95, 3–51 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Adler, I., Alizadeh, F.: Primal-dual interior point algorithms for convex quadratically constrained and semidefinite optimization problems. Technical Report RRR 46-95, RUTCOR, Rutgers University (1995)

    Google Scholar 

  3. Fischer, A., Peng, J., Terlaky, T.: A new complementarity function for P cones (2003) (Manuscript)

    Google Scholar 

  4. Fischer, A.: A special Newton-type optimization method. Optimization 24, 269–284 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, B., Harker, P.T.: A non-interior-point continuation method for linear complementarity problems. SIAM J. Matrix Anal. Appl. 14, 1168–1190 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kanzow, C.: Some noninterior continuation methods for linear complementarity problems. SIAM J. Matrix Anal. Appl. 17, 851–868 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Burke, J.V., Xu, S.: The global linear convergence of a noninterior path-following algorithm for linear complementarity problems. Math. Oper. Res. 23, 719–734 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Clarke, F.H.: Optimization and nonsmooth analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons Inc., New York (1983)

    MATH  Google Scholar 

  9. Alizadeh, F., Schmieta, S.H.: Optimization with semidefinite, quadratic and linear constraints. Technical Report RRR 23-97, RUTCOR, Rutgers University (1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan

    Yu Xia

  2. Advanced optimization Lab, Department of Computing and, Software McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    Jiming Peng

Authors
  1. Yu Xia
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  2. Jiming Peng
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Xia, Y., Peng, J. (2005). A Continuation Method for the Linear Second-Order Cone Complementarity Problem. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424925_32

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  • DOI: https://doi.org/10.1007/11424925_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25863-6

  • Online ISBN: 978-3-540-32309-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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