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Generalized Convexity and Generalized Derivatives

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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 devoted to the study of nonsmooth generalized convex functions with the help of special classes of generalized derivatives. Several results are presented on the links between generalized monotonicity of the generalized derivatives and generalized convexity of the functions under discussion. The abundance of the different notions of generalized derivatives has motivated an axiomatic treatment resulting, among others, in the concept of first order approximation. The usefulness of quasiconvex first order approximations in optimization theory is investigated, in particular, generalized upper quasidifferentiable functions are studied, quasiconvex Farkas Theorems and KKT-type optimality conditions are elaborated.

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Author information

Authors and Affiliations

  1. Faculty of Business and Economics, University of Pécs, 7622, Pécs, Hungary

    Sándor Komlósi*

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  1. Sándor Komlósi*
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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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Komlósi*, S. (2005). Generalized Convexity and Generalized Derivatives. 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_10

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