On a class of nonsmooth composite functions

Alexander Shapiro (ashapiroisye.gatech.edu)

Abstract: We discuss in this paper a class of nonsmooth functions which can be represented, in a neighborhood of a considered point, as a composition of a positively homogeneous convex function and a smooth mapping which maps the considered point into the null vector. We argue that this is a sufficiently rich class of functions and that such functions have various properties useful for purposes of optimization.

Keywords: Nonsmooth optimization, directional derivatives, semismooth functions, partially smooth functions, optimality conditions, sensitivity analysis

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Preprint, School of Industrial and Systems Engineering, Georgia Institute of Technology, July, 2002.

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Entry Submitted: 07/13/2002
Entry Accepted: 07/15/2002
Entry Last Modified: 07/26/2002

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