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Handbook of Generalized Convexity and Generalized Monotonicity pp 195–236Cite as

Generalized Convexity in Vector Optimization

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Avignon, 84000, Avignon, France

    Luc Dinh The

  2. Hanoi Institute of Mathematics, 18 Hoang Quoc Viet Road, Hanoi, Vietnam

    Luc Dinh The

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  1. Luc Dinh The
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Editor information

Editors and Affiliations

  1. University of Aegean, Greece

    Nicolas Hadjisavvas

  2. University of Pécs, Hungary

    Sándor Komlósi

  3. University of California, Riverside, USA

    Siegfried Schaible

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Dinh The, L. (2005). Generalized Convexity in Vector Optimization. In: Hadjisavvas, N., Komlósi, S., Schaible, S. (eds) Handbook of Generalized Convexity and Generalized Monotonicity. Nonconvex Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/0-387-23393-8_5

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