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Encyclopedia of Optimization pp 3659–3662Cite as

Splitting Method for Linear Complementarity Problems

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References

  1. Cottle RW, Golub GH, Sacher RS (1978) On the solution of large, structured linear complementarity problems: the block partitioned case. Appl Math Optim, 4:347–363

    Article  MathSciNet  MATH  Google Scholar 

  2. Cottle RW, Pang J-S, Stone RE (1992) The linear complementarity problem. Acad. Press, New York

    MATH  Google Scholar 

  3. Cryer CW (1971) The solution of a quadratic programming problem using systematic overrelaxation. SIAM J Control Optim, 9:385–392

    Article  MathSciNet  MATH  Google Scholar 

  4. DeLeone R, Mangasarian OL (1988) Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem. Math Program, 42:347–361

    Article  MathSciNet  Google Scholar 

  5. DePierro AR, Iusem AN (1993) Convergence properties of iterative methods for symmetric positive semidefinite linear complementarity problems. Math Oper Res, 18:317–333

    Article  MathSciNet  Google Scholar 

  6. Eckstein J, Ferris MC (1994) Operator splitting methods for monotone affine variational inequalities, with a parallel application to optimal control. Techn. Report Thinking Machines Corp

    Google Scholar 

  7. Hildreth C (1957) A quadratic programming procedure. Naval Res Logist Quart, 4:79–85

    Article  MathSciNet  Google Scholar 

  8. Keller HB (1965) On the solution of singular and semidefinite linear systems by iteration. SIAM J Numer Anal, 2:281–290

    Google Scholar 

  9. Li W (1993) Remarks on convergence of matrix splitting algorithm for the symmetric linear complementarity problem. SIAM J Optim, 3:155–163

    Article  MathSciNet  MATH  Google Scholar 

  10. Lin YY, Pang J-S (1987) Iterative methods for large convex quadratic programs: A survey. SIAM J Control Optim, 25:383–411

    Article  MathSciNet  MATH  Google Scholar 

  11. Luo Z-Q, Tseng P (1991) On the convergence of a matrix: splitting algorithm for the symmetric monotone linear complementarity problem. SIAM J Control Optim, 29:1037–1060

    Article  MathSciNet  MATH  Google Scholar 

  12. Luo Z-Q, Tseng P (1992) Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem. SIAM J Optim, 2:43–54

    Article  MathSciNet  MATH  Google Scholar 

  13. Mangasarian OL (1977) Solution of symmetric linear complementarity problems by iterative methods. J Optim Th Appl, 22:465–485

    Article  MathSciNet  MATH  Google Scholar 

  14. Mangasarian OL (1984) Sparsity-preserving SOR algorithms for separable quadratic and linear programming. Comput Oper Res, 11:105–112

    Article  MathSciNet  MATH  Google Scholar 

  15. Mangasarian OL (1991) Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem. SIAM J Optim, 1:114–122

    Article  MathSciNet  MATH  Google Scholar 

  16. Mangasarian OL, DeLeone R (1988) Parallel gradient projection successive overrelaxation for symmetric linear complementarity problems and linear programs. Ann Oper Res, 14:41–59

    Article  MathSciNet  MATH  Google Scholar 

  17. Ortega JM, Rheinboldt WC (1970) Iterative solution of nonlinear equations in several variables. Acad. Press, New York

    MATH  Google Scholar 

  18. Pang J-S (1982) On the convergence of a basic iterative method for the implicit complementarity problem. J Optim Th Appl, 37:149–162

    Article  MATH  Google Scholar 

  19. Pang J-S (1984) Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem. J Optim Th Appl, 42:1–17

    Article  MATH  Google Scholar 

  20. Pang J-S (1986) More results on the convergence of iterative methods for the symmetric linear complementarity problem. J Optim Th Appl, 49:107–134

    Article  MATH  Google Scholar 

  21. Solodov MV, Tseng P (1996) Modified projection-type methods for monotone variational inequalities. SIAM J Control Optim, 34:1814–1830

    Article  MathSciNet  MATH  Google Scholar 

  22. Tseng P (1990) Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming. Math Program, 48:249–263

    Article  MathSciNet  MATH  Google Scholar 

  23. Tseng P (1991) Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM J Control Optim, 29:119–138

    Article  MathSciNet  MATH  Google Scholar 

  24. Tseng P (1995) On linear convergence of iterative methods for the variational inequality problem. J Comput Appl Math, 60:237–252

    Article  MathSciNet  MATH  Google Scholar 

  25. Young DM (1971) Iterative solution of large linear systems. Acad. Press, New York

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department Math., University Washington, Seattle, USA

    Paul Tseng

Authors
  1. Paul Tseng
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Tseng, P. (2008). Splitting Method for Linear Complementarity Problems . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_630

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