Abstract
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, log in via an institution to check access.
Similar content being viewed by others
References
Borwein J.M., Lewis A.S.: Quasi-relative interior and duality: part I. Math. Program. 57, 15–48 (1992)
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)
Daniele, P., Giuffré, S., Idone, G., Maugeri, A.: Infinite dimensional duality and applications. Math. Ann. 339, 221–239 (2007)
Daniele P., Maugeri A.: Variational inequalities and discrete and continuum models of network equilibrium problems. Math. Comput. Model. 35, 689–708 (2002)
Daniele P., Giuffré S.: General infinite dimensional duality and applications to evolutionary networks and equilibrium problems. Optim. Lett. 1, 227–243 (2007)
Giannessi, F., Maugeri, A. (eds.): Variational Inequalities and Network Equilibrium Problems. Plenum, New York (1995)
Giannessi, F., Maugeri, A., Pardalos, P. (Eds.): Equilibrium Problems: NonSmooth Optimization and Variational Inequality Model. Nonconvex Optim. Appl., vol. 58, Kluwer, Dordrecht (2001)
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)
Giannessi, F., Maugeri, A. (Eds.): Variational Inequalities and Network Equilibrium Problems, Erice (1994), Plenum, New York (1995)
Gwinner J., Raciti F.: On a class of random variational inequalities on random sets. Numer. Funct. Anal. Optim. 27(5–6), 619–638 (2006)
Gwinner J., Raciti F.: Random equilibrium problems on networks. Math. Comput. Model. 43, 880–891 (2006)
Idone G., Maugeri A., Vitanza C.: Variational inequalities and the elastic-plastic torsion problem. J. Optim. Theory Appl. 117, 489–501 (2003)
Idone G., Maugeri A.: Variational inequalities and transport planning for an elastic and continuous model. J. Ind. Manag. Optim. 1, 81–86 (2005)
Idone G., Maugeri A., Vitanza C.: Topics on variational analysis and applications to equilibrium problems. J. Global Optim. 28, 339–346 (2004)
Jahn J.: Introduction to Nonlinear Optimization. Springer, New York (2007)
Jeyakumar V., Wolkowicz H.: Generalizations of Slater’s constraint qualification fo infinite convex programs. Math. Program. 57, 85–102 (1992)
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)
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)
Maugeri A., Raciti F.: On general infinite dimensional complementarity problems. Optim. Lett. 2(1), 71–90 (2008)
Raciti F.: Equilibrium conditions and vector variational inequalities: a complex relation. J. Global Optim. 40, 353–360 (2008)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Maugeri, A., Raciti, F. Remarks on infinite dimensional duality. J Glob Optim 46, 581–588 (2010). https://doi.org/10.1007/s10898-009-9442-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-009-9442-y