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Generalized Convexity in Vector Optimization

  • Dinh The Luc 
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 76)

Abstract

In this chapter we introduce the notion of convexity and generalized convexity including invexity for vector valued functions. Some characterizations of these functions are provided. Then we study vector problems involving generalized convex functions. The major aspects of this study concern the existence of efficient solutions, optimality conditions using contingent derivatives and approximate Jacobians, scalarization for convex and quasiconvex problems, and topological properties of efficient solution sets of generalized convex problems.

Keywords

Generalized convex vector functions efficient solutions vector optimization problems 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Dinh The Luc 
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of AvignonAvignonFrance
  2. 2.Hanoi Institute of MathematicsHanoiVietnam

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