Journal of Optimization Theory and Applications

, Volume 122, Issue 1, pp 1–17

Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities

  • M. Bianchi
  • N. Hadjisavvas
  • S. Schaible

DOI: 10.1023/B:JOTA.0000041728.12683.89

Cite this article as:
Bianchi, M., Hadjisavvas, N. & Schaible, S. Journal of Optimization Theory and Applications (2004) 122: 1. doi:10.1023/B:JOTA.0000041728.12683.89


A coercivity condition is usually assumed in variational inequalities over noncompact domains to guarantee the existence of a solution. We derive minimal, i.e., necessary coercivity conditions for pseudomonotone and quasimonotone variational inequalities to have a nonempty, possibly unbounded solution set. Similarly, a minimal coercivity condition is derived for quasimonotone variational inequalities to have a nonempty, bounded solution set, thereby complementing recent studies for the pseudomonotone case. Finally, for quasimonotone complementarity problems, previous existence results involving so-called exceptional families of elements are strengthened by considerably weakening assumptions in the literature.

Variational inequalitiesquasimonotone mapspseudomonotone mapscoercivity conditionsexceptional families of elements

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • M. Bianchi
    • 1
  • N. Hadjisavvas
    • 2
  • S. Schaible
    • 3
  1. 1.Istituto di Econometria e Matematica per le Applicazioni EconomicheFinanziarie e Attuariali, UniversitàMilanoItaly
  2. 2.Department of Product and Systems Design EngineeringUniversity of the AegeanSyrosGreece
  3. 3.A.G. Anderson Graduate School of ManagementUniversity of CaliforniaRiversideCalifornia