ISSN:
1573-2878
Keywords:
Generalized convex functions
;
generalized vector variational inequalities
;
multi-objective programming problems
;
necessary and sufficient conditions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, (α, φ,Q)-invexity is introduced, where α:X ×X → intR m + , φ: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 (α, φ,Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (α, φ,Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00940559
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