Skip to main content

Advertisement

SpringerLink
Log in

On general infinite dimensional complementarity problems

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

The aim of this paper is to present a way to study directly generalized complementarity problems in normed spaces. By means of new results on infinite dimensional Lagrange theory we show some optimality conditions which reduce the study of the problems to the one of suitable systems of equalities and inequalities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aubin J.P. and Frankowska H. (1990). Set Valued Analysis. Birkhäuser, Boston

    MATH  Google Scholar 

  2. Allen G. (1977). Variational inequalities, complementary probems and duality theorems. J. Math. Anal. Appl. 58: 1–10

    Article  MATH  MathSciNet  Google Scholar 

  3. Blum E. and Oettli W. (1994). From optimization and variational inequalities to equilibrium problems. Math. Stud. 63: 123–145

    MATH  MathSciNet  Google Scholar 

  4. Borwein J.M. and Lewis A.S. (1992). Partially finite convex programming, part I: quasi relative interiors and duality theory. Math. Program. 57: 15–48

    Article  MATH  MathSciNet  Google Scholar 

  5. Cojocaru M.G., Daniele P. and Nagurney A. (2005). Projected dynamical systems and evolutionary (time-dependent) variational inequalities via Hilbert spaces with applications. J. Optim. Theory Appl. 27(3): 1–15

    MathSciNet  Google Scholar 

  6. Cojocaru M.G., Daniele P. and Nagurney A. (2006). Double-layered dynamics: unifed theory of projected dynamical systems and evolutionary variational inequalities. Eur. J. Oper. Res. 175(1): 494–507

    Article  MATH  MathSciNet  Google Scholar 

  7. Daniele P., Maugeri A. and Oettli W. (1999). Time-dependent traffic equilibria. J. Optim. Theory Appl. 103: 543–555

    Article  MATH  MathSciNet  Google Scholar 

  8. Daniele, P., Giuffrè, S.: General infinite dimensional duality and applications to evolutionary network equilibrium problems. Optim. Lett.

  9. Doniele P., Idone G. and Maugeri A. (2003). Variational inequalities and the continuum model of transportation problem. Int. J. Nonlinear Sci. Numer. Simul. 4: 11–16

    Google Scholar 

  10. Dempster, M.A.H.: Introduction to stochastic programming. Stochastic programming. In: Proceedings of the International Conference, Oxford, pp. 3–59 (1980)

  11. Flam S.D. (1987). Approximating some convex programs in terms of Borel fields. Math. Program. Study 31: 73–78

    MATH  MathSciNet  Google Scholar 

  12. Giuffrè S., Idone G. and Maugeri A. (2005). Duality theory and optimality conditions for generalized complementarity problems. Nonlinear Anal. 63: 1655–1664

    Article  Google Scholar 

  13. Ganguly A. and Wadhwa K. (1997). On random variational inequalities. J. Math. Anal. Appl. 206: 315–321

    Article  MATH  MathSciNet  Google Scholar 

  14. Gwinner J. and Raciti F. (2006). On a class of random variational inequalities on random sets. Numer. Funct. Anal. optim. 27(5–6): 619–636

    Article  MATH  MathSciNet  Google Scholar 

  15. Gürkan G., Özge A.Y. and Robinson S.M. (1999). Sample-path solution of stochastic variational inequalities. Math. Program. 84: 313–333

    Article  MATH  MathSciNet  Google Scholar 

  16. Habetler G.J. and Price A.L. (1971). Existence theory for generalized nonlinear complementarity problems. J. Optim. Theory Appl. 7: 223–239

    Article  MATH  MathSciNet  Google Scholar 

  17. Idone G. (2004). Variational inequalities and applications to a continuum model of transportation network with capacity constraints. J. Global Optim. 28: 45–53

    Article  MATH  MathSciNet  Google Scholar 

  18. Idone G. and Maugeri A. (2004). Variational inequalities and a transport planning for an elastic and continuum model. J. Ind. Manag. Optim. 28: 45–53

    MATH  MathSciNet  Google Scholar 

  19. Isac G. (1987). Fixed point theory and complementarity problems in Hilbert space. Bull. Aust. Math. Soc. 36: 295–310

    MathSciNet  Google Scholar 

  20. Jahn J. (1996). Introduction to the theory of nonlinear optimization. Springer, Berlin

    MATH  Google Scholar 

  21. Maugeri A., Palagacev D.K. and Softova L.G. (2000). Elliptic and Parabolic Equations with Discontinuoous Coefficients. Wiley-VCH, Berlin

    Google Scholar 

  22. Noor M.A. and Oettli W. (1994). On general nonlinear complementarity problems and quasi-equilibria. Le Matematiche 49: 313–331

    MATH  MathSciNet  Google Scholar 

  23. Saigal R. (1976). Extension of the generalized complementarity problem. Math. Oper. Res. 1: 260–266

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Antonino Maugeri & Fabio Raciti

Authors
  1. Antonino Maugeri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabio Raciti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonino Maugeri.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maugeri, A., Raciti, F. On general infinite dimensional complementarity problems. Optimization Letters 2, 71–90 (2008). https://doi.org/10.1007/s11590-007-0044-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-007-0044-7

Keywords

Search

Navigation