Abstract
Convexity plays a crucial role in mathematical optimization theory. Especially, in duality theory and in constructing optimality conditions, convexity has been the most important concept since the basic reference by Rockafellar was published. Different types of generalized convexities have proved to be the main tool when constructing optimality conditions, particularly sufficient conditions for optimality. In this chapter, we analyze the properties of the generalized pseudo- and quasiconvexities for nondifferentiable locally Lipschitz continuous functions. The treatment is based on the Clarke subdifferentials and generalized directional derivatives.
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© 2014 Springer International Publishing Switzerland
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Bagirov, A., Karmitsa, N., Mäkelä, M.M. (2014). Generalized Convexities. In: Introduction to Nonsmooth Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-08114-4_5
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DOI: https://doi.org/10.1007/978-3-319-08114-4_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08113-7
Online ISBN: 978-3-319-08114-4
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