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Local Uniqueness of Solutions to the Extended Linear Complementarity Problem

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Abstract

In this paper, we study the local uniqueness of the solutions to the extended linear complementarity problem (XLCP, Ref. 1) by means of a concept which is an extension of the nondegenerate matrix in the standard LCP. Then, we give some special characterizations for the local uniqueness of the solutions to the horizontal linear complementarity problem (HLCP).

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References

  1. Mangasarian, O. L., and Pang, J. S., The Extended Linear Complementarity Problem, SIAM Journal on Matrix Analysis and Applications, Vol. 16, pp. 359–368, 1995.

    Google Scholar 

  2. Ye, Y., A Fully Polynomial-Time Approximation Algorithm for Computing a Stationary Point of the General Linear Complementarity Problem, Mathematics of Operations Research, Vol. 18, pp. 334–345, 1993.

    Google Scholar 

  3. Gowda, M. S., On the Extended Linear Complementarity Problem, Mathematical Programming, Vol. 72, pp. 33–50, 1996.

    Google Scholar 

  4. Mangasarian, O. L., Locally Unique Solutions of Quadratic Programs, Linear and Nonlinear Complementarity Problems, Mathematical Programming, Vol. 19, pp. 200–212, 1980.

    Google Scholar 

  5. Cottle, R. W., Pang, J. S., and Stone, R. E., The Linear Complementarity Problem, Academic Press, Boston, Massachusetts, 1992.

    Google Scholar 

  6. Gowda, M. S., An Analysis of Zero Set and Global Error Bound Properties of a Piecewise Affine Function via Its Recession Function, SIAM Journal on Matrix Analysis and Applications, Vol. 17, pp. 594–609, 1996.

    Google Scholar 

  7. Zhang, Y., On the Convergence of a Class of Infeasible Interior-Point Methods for the Horizontal Linear Complementarity Problem, SIAM Journal on Optimization, Vol. 4, pp. 208–227, 1994.

    Google Scholar 

  8. Sznajder, R., and Gowda, M. S., Generalizations of P 0 and P-Properties; Extended Vertical and Horizontal LCPs, Linear Algebra and Its Applications, Vols. 223/224, pp. 695–715, 1995.

    Google Scholar 

  9. Gowda, M. S., On Reducing a Monotone Horizontal LCP to an LCP, Applied Mathematics Letters, Vol. 8, pp. 97–100, 1994.

    Google Scholar 

  10. TÜtÜncÜ, R. H., and Todd, M. J., Reducing Horizontal Linear Complementarity Problems, Linear Algebra and Its Applications, Vols. 223/224, pp. 716–720, 1995.

    Google Scholar 

  11. Kanzow, C., Global Convergence Properties of Some Iterative Methods for Linear Complementarity Problems, SIAM Journal on Optimization, Vol. 6, pp. 326–341, 1996.

    Google Scholar 

  12. Tseng, P., Growth Behavior of a Class of Merit Functions for the Nonlinear Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 89, pp. 17–37, 1996.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

    J. Z. Zhang (Professor)

  2. Department of Applied Mathematics, Northern Jiaotong University, Beijing, China

    N. H. Xiu (Associate Professor)

Authors
  1. J. Z. Zhang
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  2. N. H. Xiu
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Zhang, J.Z., Xiu, N.H. Local Uniqueness of Solutions to the Extended Linear Complementarity Problem. Journal of Optimization Theory and Applications 103, 715–726 (1999). https://doi.org/10.1023/A:1021748410901

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