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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 106, No. 3, pp. 475488, SEPTEMBER 2000 On Nondifferentiable and Nonconvex
 

Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 106, No. 3, pp. 475488, SEPTEMBER 2000
On Nondifferentiable and Nonconvex
Vector Optimization Problems1
Q. H. ANSARI,2
AND J. C. YAO
3
Communicated by F. Giannessi
Abstract. In this paper, we prove the equivalence among the Minty
vector variational-like inequality, Stampacchia vector variational-like
inequality, and a nondifferentiable and nonconvex vector optimization
problem. By using a fixed-point theorem, we establish also an existence
theorem for generalized weakly efficient solutions to the vector optimiz-
ation problem for nondifferentiable and nonconvex functions.
Key Words. Variational-like inequalities, vector optimization prob-
lems, generalized solutions, subinvex functions, -subdifferential, fixed
points.
1. Introduction and Preliminaries
In the recent past, vector variational inequalities (VVI) and their
generalizations have been used as a tool to solve vector optimization prob-
lems (VOP). For details on VVI and their generalizations, we refer to Ref.

  

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

 

Collections: Mathematics