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Generalized Convexity, Generalized Monotonicity and Nonsmooth Analysis

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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

This chapter is an introduction to generalized monotone multivalued maps and their relation to generalized convex functions through subdifferential theory. In particular, it contains the characterization of various types of generalized convex functions through properties of their subdifferentials. Also, some recent results on properly quasimonotone maps, maximal pseudomonotone maps, and a new “quasiconvex” subdifferential are presented.

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Authors and Affiliations

  1. Department of Product and Systems Design Engineering, University of the Aegean, 84100, Hermoupolis, Syros, Greece

    Nicolas Hadjisavvas

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  1. Nicolas Hadjisavvas
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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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Hadjisavvas, N. (2005). Generalized Convexity, Generalized Monotonicity and Nonsmooth Analysis. 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_11

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