Journal of Optimization Theory and Applications

, Volume 124, Issue 1, pp 79–92

Coercivity Conditions for Equilibrium Problems

  • M. Bianchi
  • R. Pini

DOI: 10.1007/s10957-004-6466-9

Cite this article as:
Bianchi, M. & Pini, R. J Optim Theory Appl (2005) 124: 79. doi:10.1007/s10957-004-6466-9


The study of the existence of solutions of equilibrium problems on unbounded domains involves usually the same sufficient assumptions as for bounded domains together with a coercivity condition. We focus on two different conditions: the first is obtained assuming the existence of a bounded set such that no elements outside is a candidate for a solution; the second allows the solution set to be unbounded. Our results exploit the generalized monotonicity properties of the function f defining the equilibrium problem. It turns out that, in both the pseudomonotone and the quasimonotone setting, an equivalence can be stated between the nonemptyness and boundedness of the solution set and these coercivity conditions. In the pseudomonotone case, we compare our coercivity conditions with various coercivity conditions that appeared in the literature.


Equilibrium problemsgeneralized monotonicitygeneralized convexitycoercivity conditions

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. Bianchi
    • 1
  • R. Pini
    • 2
  1. 1.Istituto di Econometria e Matematica per le Applicazioni Economiche, Finanziarie e AttuarialiUniversità Cattolica del Sacro CuoreMilanoItaly
  2. 2.Dipartimento di Metodi Quantitativi per l’EconomiaUniversità di Milano- BicoccaMilanoItaly