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Generalized Convexity and Optimality Conditions in Scalar and 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))

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Abstract

In this chapter, the role of generalized convex functions in optimization is stressed. A particular attention is devoted to local-global properties, to optimality of stationary points and to sufficiency of first order necessary optimality conditions for scalar and vector problems. Despite of the numerous classes of generalized convex functions suggested in these last fifty years, we have limited ourselves to introduce and study those classes of scalar and vector functions which are more used in the literature.

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Authors and Affiliations

  1. Department of Statistics and Applied Mathematics, University of Pisa, Via Cosmo Ridolfi 10, 56124, Pisa, ITALY

    Cambini Alberto & Martein Laura

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  1. Cambini Alberto
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  2. Martein Laura
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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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Alberto, C., Laura, M. (2005). Generalized Convexity and Optimality Conditions in Scalar and 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_4

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