A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x*∈K such that F(x*, y) ≮0 for all y∈K. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.
Bianchi, M., Hadjisavvas, N., Schaible, S., Vector Equilibrium Problems with Generalized Monotone Bifunctions, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 1995; 92 (3): 527-542. [doi:10.1023/A:1022603406244] [http://hdl.handle.net/10807/163641]
Vector Equilibrium Problems with Generalized Monotone Bifunctions
Bianchi, Monica;
1997
Abstract
A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x*∈K such that F(x*, y) ≮0 for all y∈K. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.
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