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A splitting type algorithm for multi-valued complementarity problems

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Abstract

We consider a generalized complementarity problem whose cost mapping is multi-valued and is the sum of upper Z and antitone mappings. We suggest a simple splitting type algorithm which utilizes an extended Jacobi iteration. Its convergence is proved under mild assumptions. Preliminary results of numerical experiments confirm efficiency of the algorithm presented.

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References

  1. Cottle R.W., Pang J.S., Stone R.E.: The Linear Complementarity Problem. Academic Press, Boston (1992)

    MATH  Google Scholar 

  2. Isac G.: Complementarity Problems. Springer, Berlin (1992)

    MATH  Google Scholar 

  3. Facchinei F., Pang J.S.: Finite-dimensional Variational Inequalities and Complementarity Problems. Springer, Berlin (2003)

    Google Scholar 

  4. Konnov I.V.: Equilibrium Models and Variational Inequalities. Elsevier, Amsterdam (2007)

    MATH  Google Scholar 

  5. Nikaido H.: Convex Structures and Economic Theory. Academic Press, New York (1968)

    MATH  Google Scholar 

  6. Baiocchi C., Capelo A.: Variational and Quasivariational Inequalities. Applications to Free Boundary Problems. Wiley, New York (1984)

    MATH  Google Scholar 

  7. Lapin A.V.: Domain decomposition and parallel solution of free boundary problems. Proc. Lobachevsky Mathem. Center. 13, 90–126 (2001)

    Google Scholar 

  8. Konnov I.V.: An extension of the Jacobi algorithm for multi-valued mixed complementarity problems. Optimization 56, 399–416 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Opoitsev V.I.: Nonlinear System Statics. Nauka, Moscow (1986) (in Russian)

    Google Scholar 

  10. Konnov I.V., Kostenko T.A.: Multivalued mixed complementarity problem. Russ. Mathem. (Iz VUZ). 48(12), 26–33 (2004)

    MathSciNet  Google Scholar 

  11. Konnov I.V.: An extension of the Jacobi algorithm for the complementarity problem in the presence of multivalence. Comp. Math. Math. Phys. 45, 1127–1132 (2005)

    MathSciNet  Google Scholar 

  12. Konnov I.V.: Methods of coordinate relaxation for multivalued complementarity problems. Comp. Maths. Math. Phys. 49, 979–993 (2009)

    Article  Google Scholar 

  13. Pang J.S., Chan D.: Iterative methods for variational and complementarity problems. Math. Progr. 24, 284–313 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ortega J.M., Rheinboldt W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)

    MATH  Google Scholar 

  15. Bagrinovskii K.A.: Principles of Concordance of Planning Decisions. Nauka, Moscow (1977) (in Russian)

    Google Scholar 

  16. Konnov I.V.: Iterative algorithms for multi-valued inclusions with Z mappings. J. Comput. Appl. Math. 206, 358–365 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Tamir A.: Minimality and complementarity problems associated with Z-functions and M-functions. Math. Progr. 7, 17–31 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  18. Allevi E., Gnudi A., Konnov I.V.: An extension of the Gauss-Seidel method for a class of multi-valued complementary problems. Optim. Lett. 2, 543–553 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of System Analysis and Information Technologies, Kazan University, ul. Kremlevskaya, 18, 420008, Kazan, Russia

    Igor V. Konnov

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  1. Igor V. Konnov
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Correspondence to Igor V. Konnov.

Additional information

This work was supported by RFBR–NNSF Grant No. 07-01-92101.

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Konnov, I.V. A splitting type algorithm for multi-valued complementarity problems. Optim Lett 3, 573–582 (2009). https://doi.org/10.1007/s11590-009-0136-7

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  • DOI: https://doi.org/10.1007/s11590-009-0136-7

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