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A Note on Backward Error Analysis for Generalized Linear Complementarity Problems

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Abstract

This note extends the classical Oettli–Prager theorem to generalized linear complementarity problems.

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References

  1. A. Bachem and W. Kern, Linear Programming Duality–An Introduction to Oriented Matroids (Springer, 1992).

  2. R.W. Cottle and G.B. Dantzig, A generalization of the linear complementarity problem, J. Comb. Theory 8 (1970) 79–90.

    Google Scholar 

  3. R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem (Academic Press, 1992).

  4. B. De Schutter and B. De Moor, The extended linear complementarity problem, Math. Program. 71A (1995) 289–325.

    Google Scholar 

  5. B. De Schutter and B. De Moor, Minimal realization in the max algebra is an extended linear complementarity problem, Systems & Control Letters 25(2) (1995) 103–111.

    Google Scholar 

  6. A.A. Ebiefung and M.M. Kostreva, The generalized linear complementarity problem: Least element theory and Z–matrices, J. Glob. Optim. 11 (1997) 151–161.

    Google Scholar 

  7. W. Gerlach, Zur Lösung linearer Ungleichungssysteme bei Störung der rechten Seite und der Koeffizientenmatrix, Math. Operationsforsch. Stat., Ser. Optimization 12 (1981) 41–43.

    Google Scholar 

  8. M.S. Gowda and R. Sznajder, The generalized order linear complementarity problem, SIAM J.Matrix Anal. Appl. 15 (1994) 779–795.

    Google Scholar 

  9. J. Gwinner, Acceptable solutions of linear complementarity problems, Computing 40 (1988) 361–366.

    Google Scholar 

  10. G. Hämmerlin and K.–H. Hoffmann, Numerical Mathematics, Undergraduate Texts in Mathematics (Springer, 1991).

  11. J.J. Judice and L.N. Vicente, On the solution and complexity of a generalized linear complementarity problem, J. Glob. Optim. 4 (1994) 415–424.

    Google Scholar 

  12. D. Klatte and G. Thiere, Error bounds for solutions of linear equations and inequalities, Z. Oper. Res. 41 (1995) 191–214.

    Google Scholar 

  13. O.L. Mangasarian, A condition number of linear inequalities and equalities, Methods of Operations Research 43 (1981) 3–15.

    Google Scholar 

  14. S.R. Mohan, S.K. Neogy and R. Sridhar, The generalized linear complementarity problem revisited, Math. Programming 74A (1996) 197–218.

    Google Scholar 

  15. W. Oettli and W. Prager, Compatibility of approximate solutions of linear equaitons with given error bounds for coefficients and right–hand sides, Numer. Math. 6 (1964) 405–409.

    Google Scholar 

  16. J.–S. Pang, Error bounds in mathematical programming, Math. Programming 79B (1997) 299–332.

    Google Scholar 

  17. J. Rohn, Systems of linear interval equations, Linear Algebra and its Applications 126 (1998) 39–78.

    Google Scholar 

  18. R. Schaback, Eine rundungsgenaue Formel zur maschinellen Berechnung der Prager–Oettli–Schranke, Computing 20 (1978) 177–182.

    Google Scholar 

  19. M. Sun, Monotonicity of Mangasarian's iterative algorithm for generalized linear complementarity problems, J. Math. Anal. Appl. 144 (1989) 474–485.

    Google Scholar 

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Gwinner, J. A Note on Backward Error Analysis for Generalized Linear Complementarity Problems. Annals of Operations Research 101, 391–399 (2001). https://doi.org/10.1023/A:1010982204882

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