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Solving Linear Complementarity Problems by Imbedding

  • Andreas Fischer
Conference paper

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References

  1. Aganagic, M. (1984) Newton’s method for linear complementarity problems. Math. Programming 28: 349–362.CrossRefGoogle Scholar
  2. Clarke, F.H. (1983) Optimization and Nonsmooth Analysis. Wiley, New York.Google Scholar
  3. Fischer, A. (1992a) A special Newton-type optimization method. Optimization 24: 269–284.CrossRefGoogle Scholar
  4. Fischer, A: (1992b) A globally and locally Q-quadratically convergent Newton-type method for positive semidefinite linear complementarity problems. Technical Report MATH-NM-04-1992, Department of Mathematics, Dresden University of Technology.Google Scholar
  5. Fischer, A.; K. Schonefeld (1991) Some iterative methods for quadratic programming. Technical Report 07-09-91, Department of Mathematics, Dresden University of Technology.Google Scholar
  6. Grippo, L.; S. Lucidi (1991) A differentiable exact penalty function for bound constrained quadratic programming. Optimization 22: 557–578.CrossRefGoogle Scholar
  7. Harker, P.T.; J. S. Pang (1990) A damped Newton method for the linear complementarity problem. In: Computational Solution of Nonlinear Systems of Equations. (eds.: Allgower, G.; K. Georg), Lectures in Applied Mathematics, 26: 265–284Google Scholar
  8. Harker, P.T.; B. Xiao (1990) Newton’s method for the nonlinear complementarity problem: A B-differentiable equation approach. Mathematical Programming 48: 339–357.CrossRefGoogle Scholar
  9. Kojima, M.; Mizuno, S.; Noma, T. (1989) A new continuation method for complementarity problems with uniform P-functions. Mathematical Programming 43: 107–114.CrossRefGoogle Scholar
  10. Leder, D. (1974) Automatische Schrittweitensteuerung bei global konvergenten Einbettungsmethoden. ZAMM 54: 319–324.CrossRefGoogle Scholar
  11. Mangasarian, O. L. (1976) Equivalence of the complementarity problem to a system of nonlinear equations. SIAM J. Appl. Math. 31: 89–92.CrossRefGoogle Scholar
  12. Pang, J.S. (1990a) Newtons’s method for B-differentiable equations. Math. of Operations Res. 15: 311–34l.CrossRefGoogle Scholar
  13. Pang, J.S. (1990b) Solution differentiability and continuation of Newton’s method for variational inequality problems over polyhedral sets. JOTA 66: 121–135.CrossRefGoogle Scholar
  14. Pang, J.S. (1991) A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems. Mathematical Programming 51: 101–13l.CrossRefGoogle Scholar
  15. Robinson, S. M. (1979) Generalized equations and their solution, Part I: Basic theory. Mathematical Programming Study 10: 128–141.CrossRefGoogle Scholar
  16. Watson, L. T. (1979) Solving the nonlinear complementarity problem by a homotopy method. SIAM Journal on Control and Optimization 17: 36–46.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Andreas Fischer
    • 1
  1. 1.Department of MathematicsUniversity of TechnologyDresdenGermany

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