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Tolerance approach to sensitivity analysis in linear complementarity problems

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Abstract

In this paper, we apply the tolerance approach proposed by Wendell for sensitivity analysis in linear programs to study sensitivity analysis in linear complementarity problems. In the tolerance approach, we find the range or the maximum tolerance within which the coefficients of the right-hand side of the problem can vary simultaneously and independently such that the solution of the original and the perturbed problems have the same index set of nonzero elements.

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References

  1. Lemke, C. E., andHowson, J. T.,Equilibrium Points of Bimatrix Games, SIAM Review, Vol. 12, pp. 413–423, 1964.

    Google Scholar 

  2. Ingleton, A. W.,A Problem in Linear Inequalities, Proceedings of the London Mathematical Society, Vol. 16, pp. 519–536, 1966.

    Google Scholar 

  3. Doverspike, R. D.,Some Perturbation Results for the Linear Complementarity Problem, Mathematical Programming, Vol. 23, pp. 181–192, 1982.

    Google Scholar 

  4. Ha, C. D.,Stability of the Linear Complementarity Problem at a Solution Point, Mathematical Programming, Vol. 31, pp. 327–338, 1985.

    Google Scholar 

  5. Watson, L. T.,Some Perturbation Theorems for Q-Matrices, SIAM Journal on Applied Mathematics, Vol. 31, pp. 379–384, 1976.

    Google Scholar 

  6. Wendell, R. E.,Using Bounds on the Data in Linear Programming: The Tolerance Approach to Sensitivity Analysis, Mathematical Programming, Vol. 29, pp. 304–322, 1984.

    Google Scholar 

  7. Wendell, R. E.,The Tolerance Approach to Sensitivity Analysis in Linear Programming, Management Science, Vol. 31, pp. 564–578, 1985.

    Google Scholar 

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

    Google Scholar 

  9. Bazaraa, M. S., andShetty, C. M.,Nonlinear Programming: Theory and Algorithms, Wiley, New York, 1979.

    Google Scholar 

  10. Lemke, C. E.,Bimatrix Equilibrium Points and Mathematical Programming, Management Science, Vol. 11, pp. 681–689, 1965.

    Google Scholar 

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Authors and Affiliations

  1. AT&T Bell Laboratories, Holmdel, New Jersey

    C. D. Ha (Member of Technical Staff)

  2. School of Business, Virginia Commonwealth University, Richmond, Virginia

    S. C. Narula (Professor)

Authors
  1. C. D. Ha
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  2. S. C. Narula
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Additional information

Communicated by A. V. Fiacco

The work of the first author was completed while he was at Virginia Commonwealth University, Richmond, Virginia.

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Ha, C.D., Narula, S.C. Tolerance approach to sensitivity analysis in linear complementarity problems. J Optim Theory Appl 73, 197–203 (1992). https://doi.org/10.1007/BF00940085

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  • DOI: https://doi.org/10.1007/BF00940085

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