Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 113, No. 3, pp. 435­447, June 2002 (2002)
Characterizations of Solutions for
Vector Equilibrium Problems1,2
Q. H. ANSARI,3
I. V. KONNOV,4
AND J. C. YAO
5
Communicated by S. Schaible
Abstract. In this paper, we characterize the solutions of vector equi-
librium problems as well as dual vector equilibrium problems. We
establish also vector optimization problem formulations of set-valued
maps for vector equilibrium problems and dual vector equilibrium
problems, which include vector variational inequality problems and
vector complementarity problems. The set-valued maps involved in our
formulations depend on the data of the vector equilibrium problems,
but not on their solution sets. We prove also that the solution sets of
our vector optimization problems of set-valued maps contain or
coincide with the solution sets of the vector equilibrium problems.
Key Words. Vector optimization problems, vector equilibrium prob-
lems, dual vector equilibrium problems, set-valued maps, characteriz-

Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

Collections: Mathematics