 
Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 110, No. 3, pp. 481492, September 2001 ( 2001)
Existence of a Solution and Variational Principles
for Vector Equilibrium Problems1
Q. H. ANSARI,2
I. V. KONNOV,3
AND J. C. YAO
4
Communicated by F. Giannessi
Abstract. In this paper, we prove an existence result for a solution to
the vector equilibrium problems. Then, we establish variational prin
ciples, that is, vector optimization formulations of setvalued maps for
vector equilibrium problems. A perturbation function is involved in our
variational principles. We prove also that the solution sets of our vector
optimization problems of setvalued maps contain or coincide with the
solution sets of vector equilibrium problems.
Key Words. Existence of a solution, variational principles, vector opti
mization problems, vector equilibrium problems, setvalued maps.
1. Introduction and Preliminaries
The classical variational inequality (Ref. 1) for vectorvalued functions
is known as a vector variational inequality (VVI); it has been introduced in
