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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 110, No. 3, pp. 481492, September 2001 ( 2001) Existence of a Solution and Variational Principles
 

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 set-valued 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 set-valued 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, set-valued maps.
1. Introduction and Preliminaries
The classical variational inequality (Ref. 1) for vector-valued functions
is known as a vector variational inequality (VVI); it has been introduced in

  

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

 

Collections: Mathematics