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Journal of Convex Analysis 08 (2001), No. 2, 583--594
Copyright Heldermann Verlag 2001

Partial and Generalized Subconvexity in Vector Optimization Problems

M. Adán
Dept. of Applied Mathematics, Universidad de Castilla-La Mancha, Ciudad Real, Spain

V. Novo
Dept. of Applied Mathematics, Universidad Nacional de Educación a Distancia, Madrid, Spain

This paper studies necessary conditions of weak efficiency of a constrained vector minimization problem with equality and inequality constraints in real linear spaces. These results are obtained under generalized convexity conditions through new alternative theorems and given in linear operator rules form. We present a relaxed subconvexlikeness and generalized subconvexlikeness, and likewise, define and related to this, other new concepts such as partial subconvexlikeness and partial generalized subconvexlikeness.

Keywords: Vector optimization, weak efficiency, partial subconvexlikeness, partial generalized subconvexlikeness.

MSC: 90C26; 90C29

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