Journal of Global Optimization

, Volume 40, Issue 1, pp 353–360

Equilibrium conditions and vector variational inequalities: a complex relation

Article

DOI: 10.1007/s10898-007-9202-9

Cite this article as:
Raciti, F. J Glob Optim (2008) 40: 353. doi:10.1007/s10898-007-9202-9

Abstract

Since a look to the present literature shows that the notion of vector equilibrium is not univocally defined, the relationship between vector equilibrium problems and vector variational inequalities deserves a specific analysis, deeper than in the scalar case. We analyse and compare various definitions and clarify how they depend on the modelling of the problem under consideration. Furthermore, we show that at least one vector variational inequality formulation of the problem is possible, which is equivalent to a Wardrop-type equilibrium condition. The analysis is illustrated through the concrete example of a multiclass and multiobjective supply demand network.

Keywords

Traffic Networks Vector Variational Inequalities Pareto Optimization Multiobjective Equilibrium Problems Vector Wardrop Principle 

PACS

47H04 47H05 49J40 

Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di Catania, and Facoltà di Ingegneria dell’ Università di CataniaCataniaItaly

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