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

M. Bianchi, N. Hadjisavvas and S. Schaible
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M. Bianchi: Finanziarie e Attuariali, Università
N. Hadjisavvas: University of the Aegean
S. Schaible: University of California

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 1, No 1, 17 pages

Abstract: Abstract 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.

Keywords: Variational inequalities; quasimonotone maps; pseudomonotone maps; coercivity conditions; exceptional families of elements (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (11)

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DOI: 10.1023/B:JOTA.0000041728.12683.89

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