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On differentiability of symmetric matrix valued functions

Alexander Shapiro (ashapiro***at***isye.gatech.edu )

Abstract: With every real valued function, of a real argument, can be associated a matrix function mapping a linear space of symmetric matrices into itself. In this paper we study directional differentiability properties of such matrix functions associated with directionally differentiable real valued functions. In particular, we show that matrix valued functions inherit semismooth properties of the corresponding real valued functions.

Keywords: Matrix function, eigenvalues and eigenvectors, directional derivatives, semismooth mappings

Category 1: Convex and Nonsmooth Optimization

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

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Entry Submitted: 07/05/2002
Entry Accepted: 07/05/2002
Entry Last Modified: 07/05/2002

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