Some Classical Directional Derivatives and Their Use in Optimization

Giorgio Giorgi ()
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Giorgio Giorgi: University of Pavia

No 204, DEM Working Papers Series from University of Pavia, Department of Economics and Management

Abstract: We give an overview, in …nite-dimensioonal Euclidean spaces, of some classical directional derivatives (usual directional derivatives, Dini directional derivatives, Hadamard directional derivatives) and of some classical differentiability notions. We take into consideration some applications of the said concepts to convex and generalized convex functions, to nonsmooth unconstrained optimization problems and to nonsmooth constrained scalar and vector optimization pronlems. Also the axiomatic approach to nonsmooth analysis and nonsmooth optimization problems, proposed by K.-H. Elster and J. Thierfelder, is brie‡y considered.

Keywords: Directional derivatives; generalized directional derivatives; nonsmooth analysis; nonsmooth optimality conditions; nonsmooth vector optimization problems. (search for similar items in EconPapers)
Pages: 69
Date: 2021-10
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