Skip to main content

Remarks on infinite dimensional duality

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.


We present an improvement of a recent duality theorem and a new result which stresses the fact that the strong duality, without assumptions on the interior of the ordering cone, is related to the normal cone.

This is a preview of subscription content, access via your institution.


  1. Borwein J.M., Lewis A.S.: Quasi-relative interior and duality: part I. Math. Program. 57, 15–48 (1992)

    Article  Google Scholar 

  2. Donato M.B., Maugeri A., Milasi M., Vitanza C.: Duality theory for a dynamic Walrasian pure exchange economy. Pac. J. Optim. 4, 437–547 (2008)

    Google Scholar 

  3. Daniele, P., Giuffré, S., Idone, G., Maugeri, A.: Infinite dimensional duality and applications. Math. Ann. 339, 221–239 (2007)

    Article  Google Scholar 

  4. Daniele P., Maugeri A.: Variational inequalities and discrete and continuum models of network equilibrium problems. Math. Comput. Model. 35, 689–708 (2002)

    Article  Google Scholar 

  5. Daniele P., Giuffré S.: General infinite dimensional duality and applications to evolutionary networks and equilibrium problems. Optim. Lett. 1, 227–243 (2007)

    Article  Google Scholar 

  6. Giannessi, F., Maugeri, A. (eds.): Variational Inequalities and Network Equilibrium Problems. Plenum, New York (1995)

    Google Scholar 

  7. Giannessi, F., Maugeri, A., Pardalos, P. (Eds.): Equilibrium Problems: NonSmooth Optimization and Variational Inequality Model. Nonconvex Optim. Appl., vol. 58, Kluwer, Dordrecht (2001)

  8. Giannessi, F., Maugeri, A.: Preface [Special issue on the proceedings of the first AMS-UMI joint meeting, held in Pisa, June 12-16, 2002]. J. Global Optim. 28, 3–4 (2008)

    Google Scholar 

  9. Giannessi, F., Maugeri, A. (Eds.): Variational Inequalities and Network Equilibrium Problems, Erice (1994), Plenum, New York (1995)

    Google Scholar 

  10. Gwinner J., Raciti F.: On a class of random variational inequalities on random sets. Numer. Funct. Anal. Optim. 27(5–6), 619–638 (2006)

    Article  Google Scholar 

  11. Gwinner J., Raciti F.: Random equilibrium problems on networks. Math. Comput. Model. 43, 880–891 (2006)

    Article  Google Scholar 

  12. Idone G., Maugeri A., Vitanza C.: Variational inequalities and the elastic-plastic torsion problem. J. Optim. Theory Appl. 117, 489–501 (2003)

    Article  Google Scholar 

  13. Idone G., Maugeri A.: Variational inequalities and transport planning for an elastic and continuous model. J. Ind. Manag. Optim. 1, 81–86 (2005)

    Google Scholar 

  14. Idone G., Maugeri A., Vitanza C.: Topics on variational analysis and applications to equilibrium problems. J. Global Optim. 28, 339–346 (2004)

    Article  Google Scholar 

  15. Jahn J.: Introduction to Nonlinear Optimization. Springer, New York (2007)

    Google Scholar 

  16. Jeyakumar V., Wolkowicz H.: Generalizations of Slater’s constraint qualification fo infinite convex programs. Math. Program. 57, 85–102 (1992)

    Article  Google Scholar 

  17. Maugeri, A., Murthy, M.K.V., Trudinger, N.S. (Eds.): Preface [Variational analysis and partial differential equations. In: Memory of Sergio Campanato and Guido Stampacchia]. J. Global Optim. 40 (1–3), 1–5 (2008)

  18. Maugeri A., Oettli W., Schläger D.: A flexible form of Wardrop’s principle for traffic equilibria with side constraints. Rend. Circolo Matem. Palermo 48, 185–193 (1997)

    Google Scholar 

  19. Maugeri A., Raciti F.: On general infinite dimensional complementarity problems. Optim. Lett. 2(1), 71–90 (2008)

    Article  Google Scholar 

  20. Raciti F.: Equilibrium conditions and vector variational inequalities: a complex relation. J. Global Optim. 40, 353–360 (2008)

    Article  Google Scholar 

  21. Zarantonello E.H.: Projections on convex sets in Hilbert space and spectral theory. In: Zarantonello, E.H. (eds) Contributions to Nonlinear Functional Analysis, pp. 237–424. Academic Press, London (1971)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. Maugeri.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Maugeri, A., Raciti, F. Remarks on infinite dimensional duality. J Glob Optim 46, 581–588 (2010).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Strong duality
  • Quasi-relative interior
  • Tangent cone
  • Normal cone