Generalized convex functions and vector variational inequalities |
| |
Authors: | X Q Yang |
| |
Institution: | (1) School of Mathematics, University of New South Wales, Kensington, New South Wales, Australia |
| |
Abstract: | In this paper, (, ,Q)-invexity is introduced, where :X ×X intR
m
+
, :X ×X X,X is a Banach space,Q is a convex cone ofR
m
. This unifies the properties of many classes of functions, such asQ-convexity, pseudo-linearity, representation condition, null space condition, andV-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (, ,Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (, ,Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.The author is indebted to Dr. V. Jeyakumar for his constant encouragement and useful discussion and to Professor P. L. Yu for encouragement and valuable comments about this paper. |
| |
Keywords: | Generalized convex functions generalized vector variational inequalities multi-objective programming problems necessary and sufficient conditions |
本文献已被 SpringerLink 等数据库收录! |
|