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Generalized Convexity in Vector Optimization

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Handbook of Generalized Convexity and Generalized Monotonicity

Part of the book series: Nonconvex Optimization and Its Applications ((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.

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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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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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